CN114187046B - Programming method and system for improving option price calculation speed - Google Patents
Programming method and system for improving option price calculation speed Download PDFInfo
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Abstract
The invention discloses a programming method and a programming system for improving option price calculation speed, which have important effects of improving operation performance, saving computer calculation resource consumption and avoiding data backlog in high-frequency programming transaction. The technical proposal is as follows: starting from the Taylor formula, taking a linear estimation condition as a judgment standard and taking a classical binary tree pricing model as a core, and establishing the American option high-performance pricing method. The scheme realizes the timely update of the theoretical price by asynchronously calculating the theoretical price, the low-order Greek letters and the high-order Greek letters, and is a beneficial supplement to the existing programmed strategy trading platform. Specifically, two timers are introduced to respectively realize the aims of asynchronously calculating basic parameters and expanding Greek letters, so that the option theoretical price calculation performance can be effectively improved, the computer resource consumption is reduced, the background data backlog of a trading platform is avoided, and the delay problem caused by serial processing is solved.
Description
Technical Field
The invention relates to the field of financial software service, and is suitable for American option contract theoretical price and parameter calculation such as Greek letters in a high-frequency transaction scene.
Background
Options are important financial derivative products, and have important significance for enterprises to find product prices, hedge transaction risks, reduce transaction cost and the like. With the continuous perfection of domestic financial supervision systems and the steady development of financial capital markets, domestic multi-exchange products are successively introduced to serve entity economy, and the product types are mainly concentrated on American options. Thus, market participants need to meter the theoretical price (also known as theoretical price, the same applies below) of the American option product.
Market makers, as providers of market liquidity, often need to calculate option prices and complete newspaper and quote using high frequency data during a programmed trading process. However, unlike the European option which has an analytical solution, the American option generally has only a numerical solution and an approximate analytical solution because of its complexity in pricing. Common estimation models of numerical solutions include binary tree models, monte Carlo simulations, trigeminal tree models, and the like; common estimation models for approximate analytic solutions include BAW models, bjerksund-STENSLAND (2002) models, and the like.
Although the multi-step binary tree model can calculate the American option price more accurately, under the same hardware condition, the European option Black-Schole model needs 1 microsecond for finishing theoretical price calculation, the BAW model needs 17 microseconds, and the binary tree model (step length is 100) needs 370 microseconds. Although the performance of the approximate analytic solution models such as the BAW model is improved, the problems that the pricing result is inaccurate, the calculation performance is difficult to compare favorably with that of the Black-Schole model and the like when the option expiration date is longer exist, so that a plurality of investors still are willing to select the algorithm with larger calculation resource consumption, namely the classical binary tree model.
In investment practice, when calculating the theoretical price of option contracts (option contracts can also be abbreviated as contracts), the trading platform service end needs to recalculate the hidden fluctuation rate, the fluctuation rate model parameters, the theoretical fluctuation rate value and the theoretical price of option contracts based on market quotations. Therefore, when the server side receives multiple quotations of multiple contracts at the same time, if option contract pricing calculation is completed sequentially based on the classical binary tree model, data backlog is likely to be caused, timely updating of contract theoretical prices cannot be completed, judgment of traders on markets is affected, and potential operation risks are brought to the trading platform server side due to huge consumption of computing resources.
Typically, in an option real disc exchange, exchanges push a market every 500 milliseconds, each market change triggering a recalculation of theoretical prices. Therefore, as mentioned above, when the number of the contracts of the right of the period reaches a certain order of magnitude, the obvious calculation delay of the binary tree American-type option pricing model which is advocated by the academic world may cause that the contract pricing cannot be completed even within 500 milliseconds, and a huge calculation load is brought to the trading platform, so that traders may lose the opportunity in the high-frequency trading process.
In summary, the complexity of the American option pricing model results in problems such as slow speed, long time delay, poor performance and the like of the theoretical price. Therefore, the performance requirement of high-frequency trading cannot be met by directly adopting the standard binary tree model to estimate the options, in other words, if the option pricing model based on academia directly calculates the option price, huge load is brought to trading software, even data backlog can be caused due to insufficient computer resources, so that the option theoretical price value cannot reflect market quotation in time, and foreseeable trading cost is brought to investors.
From the technical scheme, a good programming trading platform needs to measure the theoretical price of the American option, and meanwhile, the system has the following two characteristics, namely, the system has good calculation performance, and can finish the theoretical price calculation of the American option with minimum calculation resource expenditure under the scene of high-frequency quotation; secondly, the estimation result is reliable, and the calculation result can be applied to investment practice and meets the actual demands of traders; however, the existing American option pricing algorithm in academia cannot meet the above requirements.
Therefore, there is a need in the industry to propose a high performance algorithm for American option pricing, which can solve the performance bottleneck problem caused by American option pricing.
Disclosure of Invention
The following presents a simplified summary of one or more aspects in order to provide a basic understanding of such aspects. This summary is not an extensive overview of all contemplated aspects, and is intended to neither identify key or critical elements of all aspects nor delineate the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form as a prelude to the more detailed description that is presented later.
The invention aims to solve the problems, and provides a programming method and a programming system for improving the option price calculation speed, which have important effects on improving the operation performance, saving the computer calculation resource consumption and avoiding the data backlog in high-frequency programming transactions of institution investors.
The technical scheme of the invention is as follows: the invention discloses a programming method for improving option price calculation speed, which comprises the following steps:
Judging whether to trigger the option theoretical price or the preset timer condition corresponding to the option contract parameter;
when a timer is triggered, processing of option theory price or option contract parameters is correspondingly processed, wherein the processing of option theory price and option contract parameters is based on an asynchronous mode triggered by the timer.
According to an embodiment of the programmed method for increasing the option price calculation speed of the present invention, the option contract parameters include: basic greek letters, extended greek letters, sensitivity to volatility model parameters.
According to an embodiment of the programming method for improving the option price calculation speed of the present invention, when the option contract parameters are basic greek letters and extended greek letters, the processing time of the basic greek letters and the extended greek letters respectively correspond to the threshold value of the basic parameter timer and the threshold value of the extended greek letter timer, and the processing time of the option theory price corresponds to the market change trigger.
According to an embodiment of the programming method for increasing option price calculation speed of the present invention, the processing procedure for triggering option theory price for market variation further includes:
Step 1: for option contracts, when the quotation of the option contract changes, the calculation of the price of the option contract is triggered, and the contract name of the option contract and the price parameter of the contract are input: option contract standard price, execution price, due date, risk-free interest rate, fluctuation rate, step size;
Step 2: inquiring whether effective data of the option contract exist in a storage domain according to the contract name of the option contract, wherein the effective data comprise pricing parameters, theoretical prices, basic Greek letters and extended Greek letter information, if so, acquiring the pricing parameters, the basic Greek letters and the extended Greek letter information of the option contract from the storage domain, judging whether the option contract meets a linear estimation condition, and if so, entering the processing from step 3a-1 to step 3 a-3; otherwise, enter the processing of step 3b-1 to 3 b-3;
Step 3a-1: storing the contract name and the pricing parameter of the option contract into a basic parameter update domain and an extended Greek letter update domain simultaneously;
Step 3a-2: estimating a theoretical price of the option contract based on the pricing parameters input in step 1, in the case that the contract satisfies the linear estimation condition;
Step 3a-3: outputting the theoretical price of the option contract calculated in the step 3a-2 and the basic Greek letters and the extended Greek letters in the memory domain as return values;
Step 3b-1: clearing contract name information and pricing parameter information of the option in the basic parameter update domain and the extended Greek letter update domain;
step 3b-2: calculating theoretical price, basic Greek letters and extended Greek letters of the option contract;
Step 3b-3: storing the contract name, the pricing parameters and the calculation result in step 3b-2 in a storage domain, wherein the calculation result comprises the theoretical price of the option contract, the basic greek letters and the extended greek letters;
step 3b-4: and outputting the calculation result in the step 3b-2 as a return value.
According to an embodiment of the programmed method for increasing the option price calculation speed of the present invention, for an option contract, triggering the calculation of the option price when the basic parameter timer threshold is reached and storing the basic parameters of the option contract to be updated in the memory domain, further comprises:
step 1: triggering the calculation of American option pricing when the basic parameter timer threshold is reached, and acquiring the option contract name and pricing parameters in the basic parameter update domain as input;
Step 2: calculating the number of option contracts in the basic parameter update domain, if the number is 0, the basic parameter update domain is empty, and directly returning; if the number is not 0, initializing a counter i to be 1 and entering a step 3;
step 3: reading an ith contract of a basic parameter update domain, and acquiring a contract name and a pricing parameter of a current option contract;
Step 4: calculating theoretical price and basic Greek letters of the contract according to the pricing parameters obtained in the step 3;
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Updating contract names and pricing parameters of the option contracts in the domain by the basic parameters; (2) Theoretical price and basic Greek letters calculated in the step 4; (3) original extended greek letters in the memory domain;
Step 6: let i=i+1, and repeat steps 3 to 5 when the counter i is less than or equal to the option contract number calculated in step 2;
step 7: the basic parameter update field is emptied.
According to an embodiment of the programming method for increasing the option price calculation speed of the present invention, for an option contract, when an extended greek letter timer threshold is reached, the calculation of option pricing is triggered and the extended greek letters of the contract to be updated are stored in a memory domain, further including:
step 1: triggering the calculation of American option pricing when reaching the extended Greek letter timer threshold value, and acquiring the option contract name and pricing parameters in the extended Greek letter update domain as input;
Step 2: calculating the number of option contracts in the extended Greek letter update domain; if the number is 0, the expansion parameter update domain is empty and returns directly; if the number is not 0, initializing a counter i to be 1 and entering a step 3;
step 3: reading an ith contract of an expanded Greek letter update domain, and acquiring a contract name and a pricing parameter of a current option contract;
step 4: calculating the extended Greek letters of the contract according to the pricing parameters obtained in the step 3;
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Expanding Greek letters to update contract names and pricing parameters of option contracts in an intra-domain; (2) Original theoretical price and basic Greek letters in the storage domain; (3) the expanded Greek letters obtained by calculation in the step 4;
Step 6: let i=i+1, and repeat steps 3 to 5 when the counter i is less than or equal to the option contract number calculated in step 2;
step 7: the extended greek letter update field is cleared.
The invention also discloses a programming system for improving the option price calculation speed, which comprises:
The triggering judgment module judges whether to trigger the option theory price or the preset condition of the timer corresponding to the option contract parameter;
And the asynchronous processing module is used for correspondingly processing option theory price or option contract parameters when a certain timer is triggered, wherein the processing of the option theory price and the option contract parameters is based on an asynchronous mode triggered by the timer.
According to an embodiment of the programming system for increasing option price calculation speed of the present invention, the option contract parameters include: basic greek letters, extended greek letters, sensitivity to volatility model parameters.
According to an embodiment of the programming system for improving the option price calculation speed of the present invention, when option contract parameters are basic greek letters and extended greek letters, in the configuration of the trigger judgment module, processing opportunities of the basic greek letters and the extended greek letters are respectively triggered by corresponding market variations as reaching the threshold of the basic parameter timer and reaching the threshold of the extended greek letter timer.
According to an embodiment of the programming system for increasing option price calculation speed of the present invention, in the configuration of the asynchronous processing module, the processing procedure for triggering option theory price for market variation further includes:
Step 1: for option contracts, when the quotation of the option contract changes, the calculation of the price of the option contract is triggered, and the contract name of the option contract and the price parameter of the contract are input: option contract standard price, execution price, due date, risk-free interest rate, fluctuation rate, step size;
Step 2: inquiring whether effective data of the option contract exist in a storage domain according to the contract name of the option contract, wherein the effective data comprise pricing parameters, theoretical prices, basic Greek letters and extended Greek letter information, if so, acquiring the pricing parameters, the basic Greek letters and the extended Greek letter information of the option contract from the storage domain, judging whether the option contract meets a linear estimation condition, and if so, entering the processing from step 3a-1 to step 3 a-3; otherwise, enter the processing of step 3b-1 to 3 b-3;
Step 3a-1: storing the contract name and the pricing parameter of the option contract into a basic parameter update domain and an extended Greek letter update domain simultaneously;
Step 3a-2: estimating a theoretical price of the option contract based on the pricing parameters input in step 1, in the case that the contract satisfies the linear estimation condition;
Step 3a-3: outputting the theoretical price of the option contract calculated in the step 3a-2 and the basic Greek letters and the extended Greek letters in the memory domain as return values;
Step 3b-1: clearing contract name information and pricing parameter information of the option in the basic parameter update domain and the extended Greek letter update domain;
step 3b-2: calculating theoretical price, basic Greek letters and extended Greek letters of the option contract;
Step 3b-3: storing the contract name, the pricing parameters and the calculation result in step 3b-2 in a storage domain, wherein the calculation result comprises the theoretical price of the option contract, the basic greek letters and the extended greek letters;
step 3b-4: and outputting the calculation result in the step 3b-2 as a return value.
According to an embodiment of the programming system for increasing option price calculation speed of the present invention, the configuration of the asynchronous processing module, for an option contract, triggers calculation of option pricing when a basic parameter timer threshold is reached and stores basic parameters of the option contract to be updated in a storage domain, further includes:
step 1: triggering the calculation of American option pricing when the basic parameter timer threshold is reached, and acquiring the option contract name and pricing parameters in the basic parameter update domain as input;
Step 2: calculating the number of option contracts in the basic parameter update domain, if the number is 0, the basic parameter update domain is empty, and directly returning; if the number is not 0, initializing a counter i to be 1 and entering a step 3;
step 3: reading an ith contract of a basic parameter update domain, and acquiring a contract name and a pricing parameter of a current option contract;
Step 4: calculating theoretical price and basic Greek letters of the contract according to the pricing parameters obtained in the step 3;
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Updating contract names and pricing parameters of the option contracts in the domain by the basic parameters; (2) Theoretical price and basic Greek letters calculated in the step 4; (3) original extended greek letters in the memory domain;
Step 6: let i=i+1, and repeat steps 3 to 5 when the counter i is less than or equal to the option contract number calculated in step 2;
step 7: the basic parameter update field is emptied.
According to an embodiment of the programming system for increasing the option price calculation speed of the present invention, the configuration of the asynchronous processing module, when reaching the extended greek letter timer threshold for the option contract, triggers the calculation of the option price and stores the extended greek letter of the contract to be updated in the storage domain, further includes:
step 1: triggering the calculation of American option pricing when reaching the extended Greek letter timer threshold value, and acquiring the option contract name and pricing parameters in the extended Greek letter update domain as input;
Step 2: calculating the number of option contracts in the extended Greek letter update domain; if the number is 0, the expansion parameter update domain is empty and returns directly; if the number is not 0, initializing a counter i to be 1 and entering a step 3;
step 3: reading an ith contract of an expanded Greek letter update domain, and acquiring a contract name and a pricing parameter of a current option contract;
step 4: calculating the extended Greek letters of the contract according to the pricing parameters obtained in the step 3;
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Expanding Greek letters to update contract names and pricing parameters of option contracts in an intra-domain; (2) Original theoretical price and basic Greek letters in the storage domain; (3) the expanded Greek letters obtained by calculation in the step 4;
Step 6: let i=i+1, and repeat steps 3 to 5 when the counter i is less than or equal to the option contract number calculated in step 2;
step 7: the extended greek letter update field is cleared.
Compared with the prior art, the invention has the following beneficial effects: the method is based on the Taylor formula, takes the linear estimation condition as a judgment standard, establishes the American option high-performance pricing method, and is used as the expansion and popularization of the classical binary tree pricing model, the method can accurately measure the American option theoretical price under the condition of greatly reducing the computer resource expense, and the defects that the classical binary tree model has obvious operation delay, large computer resource consumption, data backlog risk and inapplicability to high-frequency transaction are overcome.
The invention realizes the timely update of the theoretical price by asynchronously calculating the theoretical price, the low-order Greek letters and the high-order Greek letters, and is a beneficial supplement to the existing programmed strategy trading platform. Specifically, two timers (a basic parameter timer and an extended Greek letter timer) are introduced to respectively realize the goal of asynchronously calculating basic parameters and extended Greek letters, so that the option theory price calculation performance can be effectively improved, the computer resource consumption is reduced, the background data backlog of a transaction platform is avoided, and the time delay problem caused by serial processing is solved.
Drawings
The above features and advantages of the present invention will be better understood after reading the detailed description of embodiments of the present disclosure in conjunction with the following drawings. In the drawings, the components are not necessarily to scale and components having similar related features or characteristics may have the same or similar reference numerals.
FIG. 1 illustrates a flow chart of one embodiment of a programmed method of the present invention for increasing option price calculation speed.
FIG. 2 is a flow chart illustrating branching flow triggered by market changes in the method embodiment of FIG. 1.
Fig. 3 shows a flow chart of a branching flow triggered by a basic parameter timer in the method embodiment shown in fig. 1.
Fig. 4 shows a flow chart of the branching flow triggered by the extended greek letter timer in the method embodiment shown in fig. 1.
FIG. 5 illustrates a schematic diagram of one embodiment of a programming system of the present invention that increases option price calculation speed.
Detailed Description
The invention is described in detail below with reference to the drawings and the specific embodiments. It is noted that the aspects described below in connection with the drawings and the specific embodiments are merely exemplary and should not be construed as limiting the scope of the invention in any way.
Before describing the technical scheme of the invention, the terms of variables and technical terms involved in the technical scheme are explained and explained first.
Description of (one) variables
Table 1 variable description
(II) noun interpretation
1. Pricing parameters (PRICING PARAMS): is a set of necessary input parameters in the option theoretical price calculation process. In the invention, the pricing parameters refer to six parameters, namely option contract standard price, execution price, due date, risk-free interest rate, fluctuation rate and step length.
2. Basic greek letter (Basic Greeks): is the derivative of option prices with respect to the partial pricing parameters, and in the present invention, the basic greek letters include delta, gamma, vega whose business implications are illustrated in the variables of table 1. These greek letters are commonly focused on by market participants and are therefore referred to as basic greek letters.
3. Extended greek letter (Expanded Greeks): is the derivative of option prices with respect to the partial pricing parameters, and in the present invention, the extended greek letter includes theta, rho, charm, vanna, vomma, speed, zomma whose business meaning is illustrated in the variables of table 1. Market participants are less focused than the basic greek letters and are therefore referred to as extended greek letters.
4. Storage Field (Storage Field): contract names, pricing parameters, theoretical prices, basic greek letters, and extended greek letters for storing option contracts.
5. Update Field (Update Field): the contract name and the pricing parameter are used for storing waiting timing accurate calculation; basic parameter update fields (Basic params Update Field) and extended greek letter update fields (Expanded Greeks Update Field) are further defined based on this concept. The basic parameter updating field is used for storing contract names and pricing parameters of waiting time accurate calculation theoretical price and basic Greek letters; the extended greek letter update field is used to store contract names and pricing parameters for accurate calculation of extended greek letters at wait times.
6. Timer (On Timer): a time interval for controlling the accurate calculation of the relevant parameters; the basic parameter timer (Basic Params On Timer) and the extended greek letter timer (Expanded Greeks On Timer) are further defined based on this concept. The basic parameter timer is used for controlling the time interval of calculating theoretical price and basic Greek letters by adopting a classical binary tree model; the extended greek letter timer is used for controlling the calculation of the time interval of the extended greek letters by adopting a classical binary tree model.
7. Linear estimation conditions:
For option contract I, at the current time t+Deltat, marking the pricing parameters of the option contract as the price S t+Δt, the execution price K, the due date T t+Δt, the risk-free interest rate r t+Δt, the fluctuation rate sigma t+Δt and the step size steps t+Δt of the option contract; in the storage domain, the pricing parameters for the option contract are recorded as S t、K、Tt、rt、σt and steps t, respectively, if these parameters satisfy the following formulas
Tt-Tt+Δt＜0.000004|σt+Δt-σt|＜0.005
rt+Δt＝rt stepst+Δt＝stepst
The option contract is said to satisfy the linear estimation condition.
(III) theoretical basis
The core idea of the polynomials taylor formula, which is a classical computational formula in higher mathematics, is to approximate a given polynomials of a plurality of variables. In view of the simple and visual mathematical meaning and the estimation result with controllable error, the taylor formula is widely applied in practice, and the theorem is shown as follows.
The theorem states that z=f (x, y) is continuous within a certain neighborhood of point (x 0,y0) and has a continuous partial derivative of (n+1) order, (x 0+h,y0 +k) is any point within this neighborhood
Wherein the symbol is
Representing hf x(x0,y0)+kfy(x0,y0
Representation of h2fxx(x0,y0)+2hkfxy(x0,y0)+k2fyy(x0,y0)
Generally, the marking
Representation of
In investment practice, a classical binary tree model is adopted for pricing 6 pricing parameters of American options; the execution price (K) is a constant; in a short period of time (e.g., 3 seconds), the change in option contract expiration time (T) has little effect on option pricing results; the risk-free interest rate (r) is affected by macroscopic economy and hardly changes significantly within 3 seconds; in a short time, there is a possibility that the step size (steps), the target asset price (S), and the volatility (σ) of the binary tree model fluctuate even drastically.
For a certain option contract, when the pricing parameters of the option contract satisfy the linear estimation condition, i.e. the step size (steps) and the risk-free interest rate (r) of the binary tree model do not change and the target asset price (S), the fluctuation rate (σ) and the option contract due date (T) only slightly change, the calculation of the option theory price by means of the taylor formula, the theory price based on the previous calculation and the basic greek letter is efficient and reliable compared to the re-calculation of the theory price by means of the classical binary tree model.
According to the multi-element taylor formula, in combination with investment practice, the following formula (1) can be used to estimate the price of the american option when the linear estimation condition is satisfied:
The meaning of the parameters is described below. For option contract I, at time T, the six pricing parameters of the option contract are respectively designated as price S t, execution price K, expiration date T t, risk-free rate r t, volatility σ t and step size steps t of the option contract, and the option contract theoretical price at this time is designated as n (S t,σt); at time t+Δt, the pricing parameters of the option contract are respectively designated as an option contract-marked price S t+Δt, an execution price K, an expiration date T t+Δt, a risk-free interest rate r t+Δt, a fluctuation rate σ t+Δt and a step size steps t+Δt, and the option contract theory price at this time is designated as pi (S t+Δt,σt+Δt). In particular, execution price is an inherent property of option contracts and does not change over time.
For any option contract, the theoretical price of the option contract is output (1) when the market changes; (2) option contracts are basic greek letters; (3) option contracts extend greek letters. At the time point t, for option contract I, calculating the option contract theoretical price and related Greek letters for the first time, and calculating six parameters such as a classical binary tree model, a pricing parameter S t、K、σt based on the time point t to obtain (1) an option theoretical price pi (S t,σt); (2) Basic greek letters delta t、vegat、gammat of option contracts; (3) As described above, the extended greek letter thetat、rhot、charmt、vannat、vommat、speedt、zommat. of option contracts has a large calculation delay due to the classical binary tree model, and calculating the theoretical price by using the classical binary tree model for any market place can bring heavy burden and large delay to the computer, so that when the linear estimation condition is satisfied, that is, market place variation is not large, the problem can be effectively solved by linearly estimating the theoretical price of option, asynchronously calculating the basic greek letter and the extended greek letter.
Thus at the t+Δt time point, (1) calculate the theoretical price: obtaining option contract theoretical price by adopting formula (1) linear estimation based on the calculation result of the t time point and the pricing parameter of the t+delta t time point; (2) Reading basic greek letters and extended greek letters, and pushing to investors: because the market variation is not great, the basic Greek letters and the extended Greek letters obtained by the previous calculation are directly pushed; (3) And storing pricing parameters of the option contract t+delta t time point into a basic Greek letter updating field and an extended Greek letter updating field, and adopting a classical binary tree model to calculate the basic Greek letters and the extended Greek letters in a timing and asynchronous mode.
Based on the above preliminary knowledge explanation, the processing steps of an embodiment of the programming method for improving the option price calculation speed of the present invention are described in detail with reference to the flowchart shown in fig. 1.
Calculation of option prices (pricing of the option contracts), the calculation results including obtaining theoretical prices, basic greek letters, and extended greek letters.
In this embodiment, the triggering of the start of the calculation process is implemented by a market trigger, a basic parameter timer trigger, and an extended greek letter timer.
The manner of dividing into the three triggers described above is based on the following considerations: for option contracts, one-time computing of theoretical prices, basic greek letters, and extended greek letters can lead to large performance delays. Taking theta as an example, when the finite difference method is adopted to estimate the low-order Greek letter, the American option theory price needs to be calculated based on the binary tree twice, which can obviously greatly increase the operation burden, and the method is particularly suitable for the high-order Greek letter.
In combination with the fact that investors generally have higher requirements on theoretical price and timeliness of basic greek letters, and do not have strict requirements on extended greek letters, two timers (a basic parameter timer trigger and an extended greek letter timer) are introduced into the method of the embodiment to achieve the goal of asynchronously calculating basic greek letters and extended greek letters, so that algorithm performance can be effectively improved, computer resource consumption can be reduced, data backlog can be avoided, and the delay problem caused by serial processing can be overcome.
To sum up, for the American option pricing of the present embodiment, three cases are triggered by the calculation of theoretical price, basic Greek letters and extended Greek letters, respectively: (1) market variation; (2) reaching a base parameter timer threshold; (3) reaching an extended greek letter timer threshold.
The innovation point of the present invention is that the timer is registered to asynchronously calculate the option theoretical price and other parameters. In the invention, a basic parameter timer and an extended Greek letter timer are registered to realize asynchronous calculation of basic parameters and extended Greek letters; similarly, it is within the scope of the invention for the registration timer to asynchronously calculate the option theoretical price and other parameters (e.g., calculate other parameters such as sensitivity of the option theoretical price to the volatility model parameters).
The whole flow diagram is shown in figure 1; the algorithm steps of the three processes are described below, respectively.
FIG. 2 illustrates branching flow triggered by market changes in the method embodiment shown in FIG. 1. For option contract I, calculation of option pricing is triggered when the exchange pushes a new market to the programmed exchange platform.
Step 1: for option contract I, when the quotation of option contract I changes, triggering the calculation of the price of the option, inputting the contract name InstrumentID of option contract I and the price parameters of the contract: option contract standard price S t+Δt, execution price K, due date T t+Δt, risk-free rate r t+Δt, volatility σ t+Δt, step steps t+Δt, where T is the time before the change and t+Δt is the time after the change.
Step 2: inquiring whether effective data of the option contract exist in a storage domain according to the option contract name, wherein the effective data comprise pricing parameters, theoretical prices, basic Greek letters and extended Greek letter information, if so, firstly acquiring the pricing parameters, the basic Greek letters and the extended Greek letter information of the option contract from the storage domain, judging whether the option contract meets a linear estimation condition, and if so, entering the processing from the step 3a-1 to the step 3 a-3; otherwise (no valid data in the memory domain or the contract does not meet the linear estimation condition), the process of steps 3b-1 to 3b-3 is entered.
How the linear estimation condition is set is described above, but the form is not limited thereto, and it is still within the scope of the present invention to make adjustments to the judgment method and threshold value of the linear estimation condition within the error range allowed by the user.
Step 3a-1: the contract name and pricing parameters of the option contract are stored in both the basic parameter update field and the extended Greek letter update field.
Step 3a-2: in the case where the contract satisfies the linear estimation condition, the theoretical price of option contract I is estimated according to the multivariate taylor formula based on the pricing parameters input in step 1.
The multi-element taylor formula is shown in the foregoing formula (1).
Step 3a-3: and (3) outputting the theoretical price calculated in the step (3 a-2) and the basic Greek letters and the extended Greek letters in the storage domain as return values.
Step 3b-1: the option is cleared of contract name information and pricing parameter information within the basic parameter update field and the extended greek letter update field.
Step 3b-2: the theoretical price, basic greek letters and extended greek letters of option contract I are calculated using a classical binary tree model.
Furthermore, the binary tree model is merely exemplary in this embodiment, and the taylor formula may be combined with other classical option pricing algorithms, for example, combining the taylor formula with other classical pricing models (e.g., BAW) to build an american option high performance pricing algorithm still falls within the scope of the present invention.
Step 3b-3: the contract name, pricing parameters, and the calculation in step 3b-2 (the calculation contains the theoretical price of option contract I, the base greek letter, and the extended greek letter) are stored in a memory field.
Step 3b-4: and outputting the calculation result (the calculation result comprises the theoretical price of option contract I, the basic Greek letter and the extended Greek letter) in the step 3b-2 as a return value.
Fig. 3 shows a branching flow triggered by a basic parameter timer in the method embodiment shown in fig. 1. For option contract I, when the base parameter timer threshold is reached, calculation of option pricing is triggered and the base parameters of the contract to be updated are stored in the memory domain.
Step 1: when the basic parameter timer threshold is reached, triggering the calculation of American option pricing, and acquiring the option contract name and pricing parameters in the basic parameter update domain as algorithm input.
Step 2: calculating the number S of option contracts in the basic parameter update domain; if s=0, the basic parameter update domain is empty and returns directly; if S+.0, initialize counter i to 1 and go to step 3.
Step 3: and reading the ith contract of the basic parameter update domain, and acquiring the contract name and the pricing parameter of the option contract.
Step 4: and (3) calculating the theoretical price and the basic Greek letters of the contract by adopting a classical binary tree model according to the pricing parameters obtained in the step (3).
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Updating contract names and pricing parameters of the option contracts in the domain by the basic parameters; (2) The theoretical price and the basic Greek letter calculated in the step 4; (3) the original extended greek letters in the memory domain.
Step 6: let i=i+1, and repeat steps 3 to 5 when i is less than or equal to S.
Step 7: the basic parameter update field is emptied.
Fig. 4 shows a branching flow triggered by an extended greek letter timer in the method embodiment shown in fig. 1. For option contract I, when the extended Greek letter timer threshold is reached, the calculation of option pricing is triggered and the extended Greek letters of the contract to be updated are stored in the memory domain.
Step 1: when the extended Greek letter timer threshold is reached, triggering the calculation of American option pricing, and acquiring the option contract name and pricing parameters in the extended Greek letter update domain as algorithm input.
Step 2: calculating the number S of option contracts in an extended Greek letter update domain; if s=0, the extension parameter update domain is empty and returns directly; if S+.0, initialize counter i to 1 and go to step 3.
Step 3: and reading an ith contract of the extended Greek letter update domain, and acquiring the contract name and the pricing parameter of the option contract.
Step 4: and (3) calculating the extended Greek letters of the contract by adopting a classical binary tree model according to the pricing parameters obtained in the step (3).
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Expanding Greek letters to update contract names and pricing parameters of option contracts in an intra-domain; (2) Original theoretical price and basic Greek letters in the storage domain; (3) the expanded Greek letters obtained by calculation in the step 4;
Step 6: let i=i+1, and repeat steps 3 to 5 when i is less than or equal to S;
step 7: the extended greek letter update field is cleared.
Fig. 5 illustrates the principles of one embodiment of a programming system of the present invention that increases the speed of option price calculation. Referring to fig. 5, the system of the present embodiment includes: and the triggering judgment module and the asynchronous processing module.
The trigger judging module is used for judging whether to trigger the option theory price or the preset timer condition corresponding to option contract parameters (such as basic Greek letters, extended Greek letters and sensitivity related to the fluctuation rate model parameters).
The asynchronous processing module is configured to correspondingly process the option theory price or the processing of the option contract parameter when a certain timer is triggered, wherein the processing of the option theory price and the option contract parameter is based on an asynchronous manner triggered by the timer.
In one embodiment of the present invention, the timer involved in the trigger determination module includes: basic parameter timers and extended greek letter timers. The processing time of the basic Greek letters and the extended Greek letters is respectively corresponding to the threshold value of the timer reaching the basic parameters and the threshold value of the timer reaching the extended Greek letters. And the calculation processing of another option theoretical price corresponds to the triggering of market variation.
The asynchronous processing module is configured to: the method comprises the steps of calculating and processing the theoretical price of the option triggered by the corresponding market variation, triggering the processing of basic Greek letters by the corresponding threshold value reaching a basic parameter timer, and triggering the processing of the extended Greek letters by the corresponding threshold value reaching an extended Greek letter timer.
The above-mentioned specific process of the option theoretical price calculation process is the flow shown in fig. 2 in the above-mentioned method embodiment, the specific process of the basic greek letter processing is the flow shown in fig. 3 in the above-mentioned method embodiment, and the specific process of the extended greek letter processing is the flow shown in fig. 4 in the above-mentioned method embodiment. The above flow steps are described in detail in the foregoing method embodiments, and are not repeated here.
While, for purposes of simplicity of explanation, the methodologies are shown and described as a series of acts, it is to be understood and appreciated that the methodologies are not limited by the order of acts, as some acts may, in accordance with one or more embodiments, occur in different orders and/or concurrently with other acts from that shown and described herein or not shown and described herein, as would be understood and appreciated by those skilled in the art.
Those of skill would further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The various illustrative logical blocks, modules, and circuits described in connection with the embodiments disclosed herein may be implemented or performed with a general purpose processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In the alternative, the processor and the storage medium may reside as discrete components in a user terminal.
In one or more exemplary embodiments, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software as a computer program product, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a web site, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital Subscriber Line (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk (disk) and disc (disk) as used herein include Compact Disc (CD), laser disc, optical disc, digital Versatile Disc (DVD), floppy disk and blu-ray disc where disks (disk) usually reproduce data magnetically, while discs (disk) reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media.
The previous description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the spirit or scope of the disclosure. Thus, the disclosure is not intended to be limited to the examples and designs described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (6)
1. A programmed method for increasing option price calculation speed, the method comprising:
Judging whether to trigger an option theory price or a preset condition of a timer corresponding to an option contract parameter, wherein the option contract parameter comprises: the method comprises the steps of carrying out processing on basic greek letters and extended greek letters, wherein the basic greek letters comprise delta, gamma, vega, the extended greek letters comprise theta, rho, charm, vanna, vomma, speed, zomma, and when option contract parameters are the basic greek letters and the extended greek letters, the processing time of the basic greek letters and the extended greek letters respectively correspond to a threshold value reaching a basic parameter timer and a threshold value reaching an extended greek letter timer;
When a certain timer is triggered, processing option theory price or option contract parameters correspondingly, wherein the processing of the option theory price and the option contract parameters is based on an asynchronous mode triggered by the timer;
wherein, the processing procedure of triggering option theoretical price for market change further comprises:
Step 1: for option contracts, when the quotation of the option contract changes, the calculation of the price of the option contract is triggered, and the contract name of the option contract and the price parameter of the contract are input: option contract standard price, execution price, due date, risk-free interest rate, fluctuation rate, step size;
Step 2: inquiring whether effective data of the option contract exist in a storage domain according to the contract name of the option contract, wherein the effective data comprise pricing parameters, theoretical prices, basic Greek letters and extended Greek letter information, if so, acquiring the pricing parameters, the basic Greek letters and the extended Greek letter information of the option contract from the storage domain, judging whether the option contract meets a linear estimation condition, and if so, entering the processing from step 3a-1 to step 3 a-3; otherwise, enter the processing of step 3b-1 to 3 b-3;
Step 3a-1: storing the contract name and the pricing parameter of the option contract into a basic parameter update domain and an extended Greek letter update domain simultaneously;
Step 3a-2: estimating a theoretical price of the option contract based on the pricing parameters input in step 1, in the case that the contract satisfies the linear estimation condition;
Step 3a-3: outputting the theoretical price of the option contract calculated in the step 3a-2 and the basic Greek letters and the extended Greek letters in the memory domain as return values;
Step 3b-1: clearing contract name information and pricing parameter information of the option in the basic parameter update domain and the extended Greek letter update domain;
step 3b-2: calculating theoretical price, basic Greek letters and extended Greek letters of the option contract;
Step 3b-3: storing the contract name, the pricing parameters and the calculation result in step 3b-2 in a storage domain, wherein the calculation result comprises the theoretical price of the option contract, the basic greek letters and the extended greek letters;
step 3b-4: outputting the calculation result in the step 3b-2 as a return value;
triggering the calculation of option pricing when the basic parameter timer threshold is reached for the option contract, and storing the basic parameters of the option contract to be updated in a storage domain;
Wherein for option contracts, when an extended Greek letter timer threshold is reached, the calculation of option pricing is triggered and the extended Greek letters of the contract to be updated are stored in a memory domain,
Wherein, the linear estimation condition is:
For option contract I, at the current time t+Deltat, marking the pricing parameters of the option contract as the price S t+Δt, the execution price K, the due date T t+Δt, the risk-free interest rate r t+Δt, the fluctuation rate sigma t+Δt and the step size steps t+Δt of the option contract; in the storage domain, the pricing parameters for the option contract are recorded as S t、K、Tt、rt、σt and steps t, respectively, if these parameters satisfy the following formulas
rt+Δt＝rt stepst+Δt＝stepst
The option contract is said to satisfy the linear estimation condition.
2. The programmed method for increasing option price calculation speed of claim 1, wherein for an option contract, triggering the calculation of option pricing and storing the base parameters of the option contract to be updated in the memory domain when the base parameter timer threshold is reached, further comprises:
step 1: triggering the calculation of American option pricing when the basic parameter timer threshold is reached, and acquiring the option contract name and pricing parameters in the basic parameter update domain as input;
Step 2: calculating the number of option contracts in the basic parameter update domain, if the number is 0, the basic parameter update domain is empty, and directly returning; if the number is not 0, initializing a counter i to be 1 and entering a step 3;
step 3: reading an ith contract of a basic parameter update domain, and acquiring a contract name and a pricing parameter of a current option contract;
Step 4: calculating theoretical price and basic Greek letters of the contract according to the pricing parameters obtained in the step 3;
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Updating contract names and pricing parameters of the option contracts in the domain by the basic parameters; (2) Theoretical price and basic Greek letters calculated in the step 4; (3) original extended greek letters in the memory domain;
Step 6: let i=i+1, and repeat steps 3 to 5 when the counter i is less than or equal to the option contract number calculated in step 2;
step 7: the basic parameter update field is emptied.
3. The programmed method for increasing option price calculation speed of claim 1, wherein for option contracts, when an extended greek letter timer threshold is reached, triggering the calculation of option pricing and the process of storing the extended greek letters of the contract to be updated in the memory domain, further comprises:
step 1: triggering the calculation of American option pricing when reaching the extended Greek letter timer threshold value, and acquiring the option contract name and pricing parameters in the extended Greek letter update domain as input;
Step 2: calculating the number of option contracts in the extended Greek letter update domain; if the number is 0, the expansion parameter update domain is empty and returns directly; if the number is not 0, initializing a counter i to be 1 and entering a step 3;
step 3: reading an ith contract of an expanded Greek letter update domain, and acquiring a contract name and a pricing parameter of a current option contract;
step 4: calculating the extended Greek letters of the contract according to the pricing parameters obtained in the step 3;
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Expanding Greek letters to update contract names and pricing parameters of option contracts in an intra-domain; (2) Original theoretical price and basic Greek letters in the storage domain; (3) the expanded Greek letters obtained by calculation in the step 4;
Step 6: let i=i+1, and repeat steps 3 to 5 when the counter i is less than or equal to the option contract number calculated in step 2;
step 7: the extended greek letter update field is cleared.
4. A programmed system for increasing option price calculation speed, the system comprising:
The triggering judgment module judges whether to trigger the option theory price or the preset condition of a timer corresponding to option contract parameters, wherein the option contract parameters comprise: the system comprises a basic Greek letter and an extended Greek letter, wherein the basic Greek letter comprises delta, gamma, vega, the extended Greek letter comprises theta, rho, charm, vanna, vomma, speed, zomma, when option contract parameters are the basic Greek letter and the extended Greek letter, in the configuration of a trigger judgment module, the processing time of the basic Greek letter and the extended Greek letter respectively correspond to the threshold value of a timer reaching the basic parameter and the threshold value of the timer reaching the extended Greek letter, and the processing time of the option theory price corresponds to market change trigger;
the asynchronous processing module is used for correspondingly processing option theory price or option contract parameters when a certain timer is triggered, wherein the processing of the option theory price and the option contract parameters is based on an asynchronous mode triggered by the timer;
In the configuration of the asynchronous processing module, the processing procedure of triggering option theory price for market variation further comprises:
Step 1: for option contracts, when the quotation of the option contract changes, the calculation of the price of the option contract is triggered, and the contract name of the option contract and the price parameter of the contract are input: option contract standard price, execution price, due date, risk-free interest rate, fluctuation rate, step size;
Step 2: inquiring whether effective data of the option contract exist in a storage domain according to the contract name of the option contract, wherein the effective data comprise pricing parameters, theoretical prices, basic Greek letters and extended Greek letter information, if so, acquiring the pricing parameters, the basic Greek letters and the extended Greek letter information of the option contract from the storage domain, judging whether the option contract meets a linear estimation condition, and if so, entering the processing from step 3a-1 to step 3 a-3; otherwise, enter the processing of step 3b-1 to 3 b-3;
Step 3a-1: storing the contract name and the pricing parameter of the option contract into a basic parameter update domain and an extended Greek letter update domain simultaneously;
Step 3a-2: estimating a theoretical price of the option contract based on the pricing parameters input in step 1, in the case that the contract satisfies the linear estimation condition;
Step 3a-3: outputting the theoretical price of the option contract calculated in the step 3a-2 and the basic Greek letters and the extended Greek letters in the memory domain as return values;
Step 3b-1: clearing contract name information and pricing parameter information of the option in the basic parameter update domain and the extended Greek letter update domain;
step 3b-2: calculating theoretical price, basic Greek letters and extended Greek letters of the option contract;
Step 3b-3: storing the contract name, the pricing parameters and the calculation result in step 3b-2 in a storage domain, wherein the calculation result comprises the theoretical price of the option contract, the basic greek letters and the extended greek letters;
step 3b-4: outputting the calculation result in the step 3b-2 as a return value;
in the configuration of the asynchronous processing module, for option contracts, when the basic parameter timer threshold is reached, the calculation of option pricing is triggered and the basic parameters of the option contracts to be updated are stored in a storage domain;
wherein, in the configuration of the asynchronous processing module, when the timer threshold of the extended Greek letters is reached for option contracts, the calculation of option pricing is triggered and the extended Greek letters of the contracts to be updated are stored in the memory domain,
Wherein, the linear estimation condition is:
For option contract I, at the current time t+Deltat, marking the pricing parameters of the option contract as the price S t+Δt, the execution price K, the due date T t+Δt, the risk-free interest rate r t+Δt, the fluctuation rate sigma t+Δt and the step size steps t+Δt of the option contract; in the storage domain, the pricing parameters for the option contract are recorded as S t、K、Tt、rt、σt and steps t, respectively, if these parameters satisfy the following formulas
rt+Δt＝rt stepst+Δt＝stepst
The option contract is said to satisfy the linear estimation condition.
5. The system of claim 4, wherein the asynchronous processing module is configured to trigger the calculation of option pricing and store the base parameters of the option contract to be updated in the memory domain when the base parameter timer threshold is reached for the option contract, further comprising:
step 1: triggering the calculation of American option pricing when the basic parameter timer threshold is reached, and acquiring the option contract name and pricing parameters in the basic parameter update domain as input;
Step 2: calculating the number of option contracts in the basic parameter update domain, if the number is 0, the basic parameter update domain is empty, and directly returning; if the number is not 0, initializing a counter i to be 1 and entering a step 3;
step 3: reading an ith contract of a basic parameter update domain, and acquiring a contract name and a pricing parameter of a current option contract;
Step 4: calculating theoretical price and basic Greek letters of the contract according to the pricing parameters obtained in the step 3;
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Updating contract names and pricing parameters of the option contracts in the domain by the basic parameters; (2) Theoretical price and basic Greek letters calculated in the step 4; (3) original extended greek letters in the memory domain;
Step 6: let i=i+1, and repeat steps 3 to 5 when the counter i is less than or equal to the option contract number calculated in step 2;
step 7: the basic parameter update field is emptied.
6. The system of claim 4, wherein the asynchronous processing module is configured to trigger the calculation of option pricing and the storing of the extended greek letters of the contract to be updated in the memory domain when the extended greek letter timer threshold is reached for the option contract, further comprising:
step 1: triggering the calculation of American option pricing when reaching the extended Greek letter timer threshold value, and acquiring the option contract name and pricing parameters in the extended Greek letter update domain as input;
Step 2: calculating the number of option contracts in the extended Greek letter update domain; if the number is 0, the expansion parameter update domain is empty and returns directly; if the number is not 0, initializing a counter i to be 1 and entering a step 3;
step 3: reading an ith contract of an expanded Greek letter update domain, and acquiring a contract name and a pricing parameter of a current option contract;
step 4: calculating the extended Greek letters of the contract according to the pricing parameters obtained in the step 3;
Step 5: updating field information of the option contract in the storage domain as a result of: (1) Expanding Greek letters to update contract names and pricing parameters of option contracts in an intra-domain; (2) Original theoretical price and basic Greek letters in the storage domain; (3) the expanded Greek letters obtained by calculation in the step 4;
Step 6: let i=i+1, and repeat steps 3 to 5 when the counter i is less than or equal to the option contract number calculated in step 2;
step 7: the extended greek letter update field is cleared.
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