發(fā)布時(shí)間：2018-01-06 03:25

  本文關(guān)鍵詞：基于BSDE的期權(quán)定價(jià)并行算法研究　出處：《山東大學(xué)》2013年博士論文　論文類(lèi)型：學(xué)位論文

  更多相關(guān)文章： 并行算法 高性能計(jì)算 倒向隨機(jī)微分方程(BSDE) 期權(quán)定價(jià)

【摘要】：在金融工程領(lǐng)域,隨著金融市場(chǎng)的日益復(fù)雜化和多樣化,越來(lái)越多的金融問(wèn)題無(wú)法直接通過(guò)解析公式進(jìn)行求解,而需要求助于復(fù)雜的數(shù)值算法并進(jìn)行大量計(jì)算。而在金融市場(chǎng),尤其對(duì)于金融交易來(lái)講,任何時(shí)間或信息的延遲,都可能帶來(lái)巨大的經(jīng)濟(jì)損失。因此,并行計(jì)算逐漸被引入到金融工程領(lǐng)域,成為復(fù)雜的金融計(jì)算問(wèn)題得以有效、快速、精確求解的重要途徑。而期權(quán)定價(jià)問(wèn)題作為金融工程中的研究熱點(diǎn)和難點(diǎn),其相關(guān)并行算法正得到越來(lái)越多的研究和關(guān)注。 BSDE (Backward Stochastic Differential Equation)是倒向隨機(jī)微分方程的簡(jiǎn)稱(chēng),近年來(lái)在金融工程領(lǐng)域得到了廣泛的研究,并被應(yīng)用到期權(quán)定價(jià)問(wèn)題中。與目前金融業(yè)界廣泛使用的Black-Scholes公式相比,BSDE在概率模型不確定的條件下更為健壯,因此它不僅能用來(lái)進(jìn)行更精確和更合乎實(shí)際的定價(jià)計(jì)算和分析,而且可以用來(lái)幫助各種類(lèi)型的投資者進(jìn)行風(fēng)險(xiǎn)對(duì)沖及其它各類(lèi)風(fēng)險(xiǎn)分析。然而,在面向BSDE應(yīng)用問(wèn)題的研究中,雖然從不同角度給出了一些有效的數(shù)值格式,但由于其理論模型較為復(fù)雜,求解過(guò)程也不同于目前期權(quán)定價(jià)領(lǐng)域廣泛使用的PDE(Partial Differential Equation、SDE(Stochastic Differential Equation)等模型,因此目前還很少有相應(yīng)的并行算法支持。 為此,本文以金融市場(chǎng)中的期權(quán)定價(jià)為背景,圍繞BSDE數(shù)值算法的并行化問(wèn)題展開(kāi)研究。系統(tǒng)地選取了幾種典型的BSDE數(shù)值算法,通過(guò)對(duì)其計(jì)算特點(diǎn)進(jìn)行分析和比較,分別研究基于Cluster和GPU兩種不同并行體系結(jié)構(gòu)的并行算法,并應(yīng)用于期權(quán)定價(jià)中。 本文的主要研究?jī)?nèi)容和貢獻(xiàn)如下： 1)提出基于Cluster的BSDE-二叉樹(shù)期權(quán)定價(jià)并行算法 根據(jù)BSDE-二叉樹(shù)方法的計(jì)算特點(diǎn),本文從降低通信開(kāi)銷(xiāo)的角度出發(fā),提出了基于Cluster的期權(quán)定價(jià)并行算法。算法采用按塊分解的數(shù)據(jù)劃分策略,一方面保證各處理器間在進(jìn)行通信時(shí),只對(duì)邊界節(jié)點(diǎn)的數(shù)據(jù)進(jìn)行傳遞；另一方面通過(guò)多個(gè)時(shí)間步進(jìn)行一次數(shù)據(jù)傳遞的方式,避免了頻繁的數(shù)據(jù)通信。 2)提出基于GPU的BSDE-二叉樹(shù)期權(quán)定價(jià)并行算法 本文從降低全局內(nèi)存的訪問(wèn)頻率角度出發(fā),提出了基于GPU的BSDE-二叉樹(shù)期權(quán)定價(jià)并行算法。算法通過(guò)增加冗余計(jì)算量的方式,避免了每個(gè)時(shí)間步上都進(jìn)行全局內(nèi)存訪問(wèn)。并從負(fù)載均衡角度出發(fā),給出直觀分配和負(fù)載均衡分配兩種不同的數(shù)據(jù)劃分策略。與CPU串行版本相比,對(duì)于時(shí)間步數(shù)為524288的單個(gè)期權(quán)定價(jià)問(wèn)題,基于GPU的并行算法能達(dá)到200倍左右的性能提升。 3)提出基于GPU的BSDE-Theta格式期權(quán)定價(jià)并行算法 通過(guò)與BSDE-二叉樹(shù)方法之間的計(jì)算特征比較,本文基于BSDE-Theta格式,以負(fù)載均衡為重點(diǎn),提出了基于GPU的期權(quán)定價(jià)并行算法。總體上令GPU kernel負(fù)責(zé)當(dāng)前時(shí)間層上的所有節(jié)點(diǎn)計(jì)算,通過(guò)合理的任務(wù)劃分達(dá)到各線(xiàn)程之間的負(fù)載均衡。同時(shí),通過(guò)重新計(jì)算和定義當(dāng)前活躍線(xiàn)程數(shù),避免了由于節(jié)點(diǎn)數(shù)目減少而造成的同—warp內(nèi)線(xiàn)程工作量差異。實(shí)驗(yàn)結(jié)果表明,在時(shí)間步數(shù)為128、模擬路徑數(shù)為80000的情況下,該算法能獲得較CPU串行版本230倍左右的加速比。 4)提出基于Cluster的BSDE-Theta格式期權(quán)定價(jià)并行算法 基于BSDE-Theta格式,本文研究和提出了Cluster環(huán)境下的期權(quán)定價(jià)并行算法。一方面通過(guò)對(duì)每個(gè)時(shí)間層上的計(jì)算進(jìn)行數(shù)據(jù)重分配,避免了由于計(jì)算量減少而造成的任務(wù)分配不均衡；另一文而,任意時(shí)間層i的數(shù)據(jù)通信中,只對(duì)各處理器在時(shí)間層i-1上的計(jì)算所需的節(jié)點(diǎn)數(shù)據(jù)進(jìn)行傳遞,從而節(jié)約了通信成本。實(shí)驗(yàn)表明對(duì)于時(shí)間步數(shù)為64、模擬路徑數(shù)為40000的計(jì)算問(wèn)題,并行版本在32個(gè)處理器的情況下達(dá)到了29倍的加速比。 5)提出BSDE-LSM方法的GPU并行算法并應(yīng)用于高維美式期權(quán)定價(jià) 為解決基于BSDE的高維美式期權(quán)定價(jià)并行化問(wèn)題,本文基于BSDE-LSM方法,在CPU+GPU架構(gòu)下,提出了一種求解高維非線(xiàn)性BSDE的并行算法。結(jié)合BSDE-LSM算法各階段的計(jì)算時(shí)間和特點(diǎn),基于GPU設(shè)計(jì)和實(shí)現(xiàn)路徑生成、終端條件計(jì)算、倒向計(jì)算階段的加速算法,利用CPU完成最終解計(jì)算階段的工作。對(duì)于GPU上各階段的加速算法設(shè)計(jì),在對(duì)計(jì)算任務(wù)進(jìn)行合理劃分的同時(shí),綜合GPU的線(xiàn)程同步特征、數(shù)據(jù)存取方法等多方面因素,使總體計(jì)算性能得到較大提升。 在未來(lái)工作中,將基于本文的研究成果,在基于BSDE-二叉樹(shù)方法和BSDE-Theta格式的多維期權(quán)定價(jià)并行化、基于GPU集群的多期權(quán)定價(jià)并行算法以及不同算法間的實(shí)驗(yàn)分析與比較方面,展開(kāi)進(jìn)一步研究。
[Abstract]:In the field of financial engineering, as financial markets become increasingly complex and diversified, more and more financial problems cannot be directly solved by analytic formula, and the need to resort to numerical algorithm for complex and large amount of calculation. And in the financial markets, especially for financial transactions, any time delays or information, may have a huge economic losses. Therefore, parallel computing has gradually been introduced into the field of financial engineering, financial become complex computing problems effectively, fast and accurate solution. An important way and option pricing problems as financial research hotspots and difficulties in engineering, the parallel algorithm is getting more and more research and attention.
BSDE (Backward Stochastic Differential Equation) is a backward stochastic differential equation, in recent years in the field of financial engineering has been widely studied, and is applied to option pricing problem. Compared with the Black-Scholes formula currently widely used in the financial industry, BSDE uncertainty in probability model under the condition of more robust, so it can not only used for pricing calculation and analysis more accurate and more practical, and can be used to help all types of investors to hedge risk and other risks analysis. However, in the BSDE by the research of the problem, although gives some effective numerical schemes from different angles, but because of its complicated theoretical model, solution the process is different from the currently widely used in the field of option pricing PDE (Partial Differential Equation SDE (Stochastic Differential Equation) mode So far, there are few parallel algorithm support.
Therefore, this article in option pricing in financial markets as the background, focuses on the research of parallel BSDE numerical algorithm. The system selects several typical BSDE numerical algorithm, through the analysis and comparison of the data, Cluster and GPU respectively on two different parallel algorithms based on parallel architecture, and application in the option pricing.
The main research contents and contributions of this paper are as follows:
1) proposed BSDE- two fork tree option pricing parallel algorithm based on Cluster
According to the calculation characteristics of BSDE- two binary tree method, this article from the perspective of reducing communication overhead, parallel algorithm is proposed based on Cluster option pricing. The algorithm uses the block decomposition according to the data partitioning strategy, one hand to ensure that each processor in communication, only the boundary node data transfer; on the other hand by more than one time step for a data transfer way, avoid frequent data communication.
2) proposed BSDE- two fork tree option pricing parallel algorithm based on GPU
From the angle of reducing access frequency of global memory, put forward the GPU BSDE- two binary tree option pricing algorithm based on parallel algorithm. By increasing the computational redundancy, avoid each time step of global memory access. And starting from the angle of load balancing, to direct allocation and load balancing two different the data partitioning strategy. Compared with the CPU serial version, for the number of time steps for a single option pricing 524288, GPU parallel algorithm can achieve the performance of 200 times based on lifting.
3) a parallel algorithm for pricing option pricing in BSDE-Theta format based on GPU
Comparing with BSDE- features between the two binary tree method, based on the BSDE-Theta format, based on load balance as the key point, parallel algorithm is proposed based on GPU option pricing. In general GPU kernel is responsible for all nodes in the current time layer calculation, achieve load balance between threads through the rational division of tasks. At the same time, through the re calculation and definition of the number of threads currently active, to avoid the decrease in the number of nodes caused by the same thread within the warp workload difference. The experimental results show that the simulation time step number is 128, the number of paths is 80000 cases, the algorithm can obtain the speedup is CPU serial version of 230 times.
4) a parallel algorithm for pricing option pricing in BSDE-Theta format based on Cluster
Based on the BSDE-Theta format, this paper studies and puts forward the option pricing under the environment of Cluster parallel algorithm. On the one hand through the redistribution of the data layer is calculated for each time, to avoid the unbalanced assignment due to the amount of calculation is reduced; the other, at any time I in the data communication layer, node data only the calculation of each processor in time on the I-1 layer to transfer, thus saving the cost of communication. Experimental results show that for the time step number is 64, the number of paths is 40000 simulation calculation, the parallel version in the case of 32 processors achieves a speedup of 29 times.
5) a GPU parallel algorithm based on BSDE-LSM method is proposed and applied to the pricing of high dimensional American options
In order to solve the parallel problem of high dimension American option pricing model based on BSDE, based on the method of BSDE-LSM, under the framework of CPU+GPU, proposed a parallel algorithm for solving high dimensional nonlinear BSDE. Combined with the characteristics of each stage and the computation time of BSDE-LSM algorithm, GPU design and implementation of path generation based on terminal condition calculation, backward acceleration algorithm the calculation stage, using CPU to complete the final calculation phase. To speed up the algorithm design of GPU stages, the reasonable division of the computational tasks at the same time, the characteristics of GPU thread synchronization, multi factor data access method, so that the overall computing performance has been greatly improved.
In the future work, based on the research results in this paper, we will further study the parallelization of multi-dimensional option pricing based on BSDE- two fork tree method and BSDE-Theta format, and multi option pricing parallel algorithm based on GPU cluster and experimental analysis and comparison among different algorithms.

【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類(lèi)號(hào)】：O211.63;TP338.6;F830.9

【引證文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 楊旭;基于GPU的自適應(yīng)波束形成處理器研究[D];南京理工大學(xué);2014年

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本文編號(hào)：1386086