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Sequential Monte Carlo Pricing of American-Style Options under Stochastic Volatility Models

The Annals of Applied Statistics, 4(1), 222-265 (2010)

43 Pages Posted: 25 Jul 2013  

Bhojnarine R. Rambharat

Office of the Comptroller of the Currency

A. E. Brockwell

Carnegie Mellon University - Department of Statistics

Date Written: June 19, 2009

Abstract

We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic programming problem can be expressed as functions of conditional distributions of volatility, given observed data. By constructing statistics summarizing information about these conditional distributions, one can obtain high quality approximate solutions. Although the required conditional distributions are in general intractable, they can be arbitrarily precisely approximated using sequential Monte Carlo schemes. The drawback, as with many Monte Carlo schemes, is potentially heavy computational demand. We present two variants of the algorithm, one closely related to the well-known least-squares Monte Carlo algorithm of Longstaff and Schwartz (2001), and the other solving the same problem using a “brute force” gridding approach. We estimate an illustrative SV model using Markov chain Monte Carlo (MCMC) methods for three equities. We also demonstrate the use of our algorithm by estimating posterior distributions of the market price of volatility risk for each of the three equities.

Keywords: Arbitrage, Risk-neutral, Dynamic programming, Optimal stopping, Decision, Latent volatility, Volatility risk premium; Grid; Sequential, Monte Carlo, MCMC

JEL Classification: C10, C13, C15, C22, C61, C63, G13

Suggested Citation

Rambharat, Bhojnarine R. and Brockwell, A. E., Sequential Monte Carlo Pricing of American-Style Options under Stochastic Volatility Models (June 19, 2009). The Annals of Applied Statistics, 4(1), 222-265 (2010). Available at SSRN: https://ssrn.com/abstract=2296951

Bhojnarine R. Rambharat (Contact Author)

Office of the Comptroller of the Currency ( email )

400 7th Street SW
Mail-stop 6E-2
Washington, DC 20219
United States

HOME PAGE: http://www.occ.gov/topics/economics/economics-staff/bios/ricky-rambharat-bio.html

A. E. Brockwell

Carnegie Mellon University - Department of Statistics ( email )

Pittsburgh, PA 15213-3890
United States

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