Volume 1, Issue 1
Memory-Reduction Method for Pricing American-Style Options under Exponential Lévy Processes

Raymond H. Chan & Tao Wu

East Asian J. Appl. Math., 1 (2011), pp. 20-34.

Published online: 2018-02

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  • Abstract

This paper concerns the Monte Carlo method in pricing American-style options under the general class of exponential Lévy models. Traditionally, one must store all the intermediate asset prices so that they can be used for the backward pricing in the least squares algorithm. Therefore the storage requirement grows like $O(mn)$, where m is the number of time steps and n is the number of simulated paths. In this paper, we propose a simulation method where the storage requirement is only $O(m+n)$. The total computational cost is less than twice that of the traditional method. For machines with limited memory, one can now enlarge m and n to improve the accuracy in pricing the options. In numerical experiments, we illustrate the efficiency and accuracy of our method by pricing American options where the log-prices of the underlying assets follow typical Lévy processes such as Brownian motion, lognormal jump-diffusion process, and variance gamma process.

  • Keywords

American options, Monte Carlo simulation, memory reduction, exponential Lévy processes.

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-1-20, author = {}, title = {Memory-Reduction Method for Pricing American-Style Options under Exponential Lévy Processes}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {1}, number = {1}, pages = {20--34}, abstract = {

This paper concerns the Monte Carlo method in pricing American-style options under the general class of exponential Lévy models. Traditionally, one must store all the intermediate asset prices so that they can be used for the backward pricing in the least squares algorithm. Therefore the storage requirement grows like $O(mn)$, where m is the number of time steps and n is the number of simulated paths. In this paper, we propose a simulation method where the storage requirement is only $O(m+n)$. The total computational cost is less than twice that of the traditional method. For machines with limited memory, one can now enlarge m and n to improve the accuracy in pricing the options. In numerical experiments, we illustrate the efficiency and accuracy of our method by pricing American options where the log-prices of the underlying assets follow typical Lévy processes such as Brownian motion, lognormal jump-diffusion process, and variance gamma process.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.020310.120410a}, url = {http://global-sci.org/intro/article_detail/eajam/10894.html} }
TY - JOUR T1 - Memory-Reduction Method for Pricing American-Style Options under Exponential Lévy Processes JO - East Asian Journal on Applied Mathematics VL - 1 SP - 20 EP - 34 PY - 2018 DA - 2018/02 SN - 1 DO - http://doi.org/10.4208/eajam.020310.120410a UR - https://global-sci.org/intro/article_detail/eajam/10894.html KW - American options, Monte Carlo simulation, memory reduction, exponential Lévy processes. AB -

This paper concerns the Monte Carlo method in pricing American-style options under the general class of exponential Lévy models. Traditionally, one must store all the intermediate asset prices so that they can be used for the backward pricing in the least squares algorithm. Therefore the storage requirement grows like $O(mn)$, where m is the number of time steps and n is the number of simulated paths. In this paper, we propose a simulation method where the storage requirement is only $O(m+n)$. The total computational cost is less than twice that of the traditional method. For machines with limited memory, one can now enlarge m and n to improve the accuracy in pricing the options. In numerical experiments, we illustrate the efficiency and accuracy of our method by pricing American options where the log-prices of the underlying assets follow typical Lévy processes such as Brownian motion, lognormal jump-diffusion process, and variance gamma process.

Raymond H. Chan & Tao Wu. (1970). Memory-Reduction Method for Pricing American-Style Options under Exponential Lévy Processes. East Asian Journal on Applied Mathematics. 1 (1). 20-34. doi:10.4208/eajam.020310.120410a
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