Double-Exponential Fast Gauss Transform Algorithms for Pricing Discrete Lookback Options
Double-Exponential Fast Gauss Transform Algorithms for Pricing Discrete Lookback Options
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DOI：
10.2977/prims/1145474605
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发表时间：
2005-12
影响因子：
1.2
通讯作者：
Yusaku Yamamoto
中科院分区：
文献类型：
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作者：
Yusaku Yamamoto
本文提出了计算离散采样回顾期权价格的快速准确算法。在Black-Scholes框架下，离散回望期权的定价可以简化为一系列高斯分布函数的卷积。利用这一事实，一个有效的算法，计算这些卷积的双指数积分公式和快速高斯变换的组合，最近已经提出。我们将该算法推广到默顿跳跃扩散模型下的回望期权和美式回望期权。数值实验表明，我们的方法是更快，更准确地比传统的方法在默顿的模型下回望选项。对于美式回望期权，当要求的精度相对较高时，我们的方法优于传统方法。
This paper presents fast and accurate algorithms for computing the prices of discretely sampled lookback options. Under the Black-Scholes framework, the pricing of a discrete lookback option can be reduced to a series of convolutions of a function with the Gaussian distribution. Using this fact, an efficient algorithm, which computes these convolutions by a combination of the double-exponential integration formula and the fast Gauss transform, has been proposed recently. We extend this algorithm to lookback options under Merton’s jump-diffusion model and American lookback options. Numerical experiments show that our method is much faster and more accurate than conventional methods for lookback options under Merton’s model. For American lookback options, our method outperforms conventional methods when required accuracy is relatively high.