Efficient Convergent Lattice Method for Asian Options Pricing with Superlinear Complexity
首发时间:2014-06-24
Abstract:Asian options have payoffs that depend strongly on the historical information of the underlying asset price. Although approximated closed formformulas are available with various assumptions, most them do not guarantee the convergence. Thus, binomial tree and PDE methods are two popularnumerical solutions for pricing. However, either the PDE method or binomial tree method has the complexity of $O(N^2)$ at least, where $N$ is thenumber of time steps. This paper proposes a first convergent lattice method with the complexity of $O(N^{1.5})$ based on the willow tree methodcite{Curran01}. The corresponding convergence rate and error bounds are also analyzed. It shows that our proposed method can provide the sameaccuracy as the PDE and binomial tree method, but requires much less computational time. When a quick pricing is required, our method can give the price with precision in a penny less than half second. Finally, numerical results supports our claims.
keywords: European Asian option pricing, Willow tree model, Interpolation, Binomial tree, Monte Carlo method.
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亚式期权定价的快速收敛超线性数值方法
摘要:亚式期权的收益与标的资产的历史信息有关。大多数近似格式解析方法需要很多假设条件,而且很难保证收敛性。二叉树和PDE方法是两种非常普遍的数值方法。但是,它们的计算速度最快能够达到$O(N^2)$,其中 $N$是时间步数。本文基于柳树模型cite{Curran01},首次提出了一种只需 $O(N^{1.5})$收敛的数值定价方法,并且分析了收敛率和误差界。数值实验表明,柳树法减少了大量计算时间,同时保证了计算精度与二叉树和PDE方法相同。
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