A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options
A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options
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DOI：
10.1287/opre.1050.0219
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发表时间：
2005-09
期刊：
影响因子：
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通讯作者：
M. Broadie;Yusaku Yamamoto
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文献类型：
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作者：
M. Broadie;Yusaku Yamamoto
本文开发了离散采样障碍，回顾和后见之明期权和离散可执行美式期权的定价算法。在Black-Scholes框架下，这些期权的定价可以简化为对高斯分布和已知函数的一系列卷积的评估。我们使用双指数积分公式和快速高斯变换有效地计算这些卷积。所得算法的计算复杂度为O（nN），其中监测/执行日期的数量为n，每个日期的样本点数量为N，并且我们的结果表明误差随N呈指数下降。我们还扩展的方法，并提供Merton的对数正态跳跃扩散模型的结果。
This paper develops algorithms for the pricing of discretely sampled barrier, lookback, and hindsight options and discretely exercisable American options. Under the Black-Scholes framework, the pricing of these options can be reduced to evaluation of a series of convolutions of the Gaussian distribution and a known function. We compute these convolutions efficiently using the double-exponential integration formula and the fast Gauss transform. The resulting algorithms have computational complexity of O(nN), where the number of monitoring/exercise dates is n and the number of sample points at each date is N, and our results show the error decreases exponentially with N. We also extend the approach and provide results for Merton's lognormal jump-diffusion model.