An Analytic Valuation Method for Multivariate Contingent Claims with Regime-Switching Volatilities

Opertations Research Letters, Vol. 39, Issue 3, 2011

Posted: 25 Mar 2009 Last revised: 22 Aug 2011

See all articles by Bong-Gyu Jang

Bong-Gyu Jang

Pohang University of Science and Technology (POSTECH)

Kum-Hwan Roh

Korea Advanced Institute of Science and Technology (KAIST), Department of Mathematical Science

Ji Hee Yoon

University College London - Department of Economics

Date Written: March 25, 2009

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 the stochastically-changing market condition. 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 closed-form valuation formulas for quanto options and exchange options with two underlying assets, as examples. In addition, we develop an approximation formula for valuing a wide range of financial contingent claims written on more than two underlying assets.

Keywords: Multivariate Contingent Claim, Drivative Pricing, Regime Switch, Business Cycle, Stochastic Volaltility

JEL Classification: C63, G13

Suggested Citation

Jang, Bong-Gyu and Roh, Kum-Hwan and Yoon, Ji Hee, An Analytic Valuation Method for Multivariate Contingent Claims with Regime-Switching Volatilities (March 25, 2009). Opertations Research Letters, Vol. 39, Issue 3, 2011. Available at SSRN: https://ssrn.com/abstract=1368107

Bong-Gyu Jang (Contact Author)

Pohang University of Science and Technology (POSTECH) ( email )

77 Cheongam-ro
Pohang
Korea, Republic of (South Korea)

Kum-Hwan Roh

Korea Advanced Institute of Science and Technology (KAIST), Department of Mathematical Science ( email )

373-1 Kusong-dong
Yuson-gu
Taejon 305-701, 130-722
Korea, Republic of (South Korea)

Ji Hee Yoon

University College London - Department of Economics ( email )

Drayton House, 30 Gordon Street
30 Gordon Street
London, WC1H 0AX
United Kingdom

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