An analytic valuation method for multivariate contingent claims with regime-switching volatilities

Authors:
Ji Hee Yoon;Bong-Gyu Jang;Kum-Hwan Roh
Affiliations:
KIS Pricing, Inc., Seoul, 150-885, Republic of Korea;Department of Industrial and Management Engineering, POSTECH, Pohang, 790-784, Republic of Korea;MiraeAsset Security Company, Seoul, 150-743, Republic of Korea
Venue:
Operations Research Letters
Year:
2011

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Abstract

In this paper, we provide an analytic valuation method for European-type contingent claims written on multiple assets in a stochastic market environment. We employ a two-state Markov regime-switching volatility in order to reflect stochastically changing market conditions. The method is developed by exploiting the probability density of the occupation time for which the underlying asset processes are in a certain regime during a time period. In order to show its usefulness, we derive analytic valuation formulas for quanto options and exchange options with two underlying assets, as examples.