30 Pages Posted: 7 Dec 2007 Last revised: 3 Oct 2012
Date Written: December 1, 2007
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: 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