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American Options Under Stochastic Volatility

30 Pages Posted: 7 Dec 2007 Last revised: 3 Oct 2012

Arun Chockalingam

Eindhoven University of Technology (TUE) - Department of Industrial Engineering and Innovation Sciences

Kumar Muthuraman

University of Texas at Austin - McCombs School of Business

Date Written: December 1, 2007

Abstract

The problem of pricing an American option written on an underlying asset with constant price volatility has been studied extensively in literature. Real-world data, however, demonstrates that volatility is not constant and stochastic volatility models are used to account for dynamic volatility changes. Option pricing methods that have been developed in literature for pricing under stochastic volatility focus mostly on European options. We consider the problem of pricing American options under stochastic volatility which has relatively had much less attention from literature. First, we develop an exercise-policy improvement procedure to compute the optimal exercise policy and option price. We show that the scheme monotonically converges for various popular stochastic volatility models in literature. Second, using this computational tool, we explore a variety of questions that seek insights into the dependence of option prices, exercise policies and implied volatilities on the market price of volatility risk and correlation between the asset and stochastic volatility.

Keywords: American option, stochastic volatility, free boundary

JEL Classification: G12, C63

Suggested Citation

Chockalingam, Arun and Muthuraman, Kumar, American Options Under Stochastic Volatility (December 1, 2007). McCombs Research Paper Series No. IROM-10-08. Available at SSRN: https://ssrn.com/abstract=1066581

Arun Chockalingam

Eindhoven University of Technology (TUE) - Department of Industrial Engineering and Innovation Sciences ( email )

Den Dolech 2
Eindhoven
Eindhoven, 5600 MB
Netherlands

HOME PAGE: http://home.tm.tue.nl/achockal/

Kumar Muthuraman (Contact Author)

University of Texas at Austin - McCombs School of Business ( email )

Austin, TX 78712
United States

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