Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc.

Published online July 28, 2022

Copyright © The Korean Mathematical Society.

Pricing American lookback options under a stochastic volatility model

Donghyun Kim, Junhui Woo, and JiHun Yoon

Pusan National University, Financial Engineering Group KIS Pricing. INC

Abstract

In this study, we deal with American lookback option prices on dividend-paying assets under a stochastic volatility (SV) model. By Laplace-Carson transform (LCT), we derive the explicit formula for the option prices and the free boundary values with a finite expiration whose volatility is driven by a fast mean-reverting the Ornstein-Uhlenbeck process. In addition, we examine the numerical implications of the SV on the American lookback option with respect to the model parameters and verify that the obtained explicit analytical option price has been obtained accurately and efficiently in comparison with the price obtained from the Monte-Carlo simulation.

Keywords: American Lookback Options; Stochastic Volatility; LaplaceCarson Transform; Monte-Carlo simulation

MSC numbers: 60H35, 91G80

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