Research On Parallel Algorithms For Option Pricing Based On Bsde

In the field of financial engineering, with the development of complication and diversity in financial markets, more and more financial problems can’t be solved directly by analytic formulas. In order to solve these problems, we must resort to complicated numerical algorithms which occupy much more computation time. Howvever, in financial markets, any delay of time or information can lead to huge economic loss, especially in the financial trading. Therefore, parallel computing is gradually introduced to the field of financial engineering and becomes an important way to solve financial problems efficiently, quickly and precisely. As a research hot spot and difficulty among the financial engineering problems, option pricing and its parallel algorithms are getting more and more study and attention.The BSDE is the abbreviation of the Backward Stochastic Differential Equation. In recent years, the theory of BSDEs is widely studied in financial engineering area and applied to option pricing problems. Compared with the Black-Scholes formula which is mow widely used in financial industry, the BSDE appears as a more robust tool to fit in the uncertainty of probability model, thus it can be used not only to perform more accurate calculations for the pricing of the financial derivatives, but also to help different investors to make more rational decisions in risk hedging and risk analysis. However, the theoretical model of the BSDE is relatively complicated, and the solution process is different with the PDE (Partial Differential Equation) and SDE (Stochastic Differential Equation) which are now widely used in the option pricing area. Thus, although some effective numerical schemes are proposed from different point of views for the BSDE application, related parallel algorithms based on the BSDE are very few.Therefore, with the background of option pricing in financial markets, this dissertation focuses on the parallelization of numerical methods for the BSDEs. Several representive numerical methods to solve the BSDEs are choosed. By analyzing and comparing their computation characteristics, the parallel algorithms are studied respectively under two different kinds of parallel architecutres including the Cluster and the GPU, and applied to the option pricing.The main research contents and contributions of this dissertation are as follows: 1) Propose a Cluster-based parallel algorithm for option pricing with the BSDE-Binomial Tree methodAccording to the computation characteristics of the BSDE-Binomial Tree method, we propose a Cluster-based parallel algorithm for option pricing from the view of reducing the communication cost. By using a block allocation strategy, the parallel algorithm on the one hand ensures the processors to transmit only the boundary nodes data; on the other hand avoid frequent communication by performing the data transmission within multiple time steps.2) Propose a GPU-based parallel algorithm for option pricing with the BSDE-Binomial Tree methodFrom the view of reducing the access frequency to the global memory, we propose a GPU-based parallel option pricing algorithm with the BSDE-Binomial Tree method. The access to the global memory on every time step is avoided by performing redundant computation. More over, two different data allocation strategies such as intuitive allocation and load-balanced allocation are proposed with the consideration of load balance. For the single option pricing problem with524288time steps, the GPU version can achieve a speedup of about200compared with the CPU serial verison.3) Propose a GPU-based parallel algorithm for option pricing with the BSDE-Theta SchemeBy comparing the computation characteristics with the BSDE-Binomial Tree method, we lay emphasis on the load balance and propose a GPU algorithm for option pricing based on the BSDE-Theta Scheme. In general, the GPU kernel takes charge of the computation of all the nodes on the current time step, and the computation tasks are distributed evenly among threads. Moreover, as the number of nodes decreases with the processing of the backward calculation, we recount and redefine the number of active threads before the kernel invocation to avoid the imbalance of the computation tasks among threads within a warp. The experimental results show that the GPU version can achieve a speedup of about230compared with the CPU serial verion when the number of time steps and simulation paths are respectively128and80000.4) Propose a Cluster-based parallel algorithm for option pricing with the BSDE-Theta SchemeBased on the BSDE-Theta Scheme, we study and propose a Cluster-based parallel algorithm for option pricing. On the one hand, the task allocation imbalance caused by the decrease of the computation amount is avoided by reallocating the nodes on each time level. On the other hand, in order to save the communication cost, only the data required by the time level M are transmitted during the communication on an arbitrary time level i. Experimental results show that the parallel version achieves a speedup of29for the problem with64time steps and40000simulation paths.5) Propose a GPU-based parallel algorithm for BSDE-LSM method with application in high dimensional American option pricingIn order to solve the parallelization problem based on the BSDE for high dimensional American option pricing, we propose a parallel algorithm to solve high dimensional non-linear BSDE based on the BSDE-LSM method under the CPU+GPU architecture. According to the computation time and characteristics of different phases of the BSDE-LSM method, we design and implement the GPU-based acceleration algorithms respectively for the path generation phase, the terminal condition calculation phase and the backward calculation phase, and perform the final solution phase on the CPU. For the design of the GPU acceleration algorithms for different phases, multiple factors which affect the parallel performance, such as the task allocation strategy, the thread synchronization feature and the data store/access method, etc. are taken into consideration, and the general performance is greatly enhanced.In future work, on the basis of the present research results, the parallelization of BSDE-Binomial Tree and BSDE-Theta Scheme based multi-dimensional BSDE solution, the GPU-cluster-based parallel algorithms for multi options pricing, as well as the experimental analysis and comparison among different algorithms will be further studied.