April 2006
We
introduce a new method to price American-style options on underlying
investments governed by stochastic volatility models. The method
combines a standard gridding approach to solving the
associated dynamic programming problem, with a sequential Monte Carlo
scheme to estimate required posterior distributions of the latent
volatility process. The method represents a refinement of
previous algorithms since it does not require the volatility process to
be directly observable. Instead, the sequential Monte Carlo
scheme provides accurate estimates of the required conditional
distributions. Furthermore, the method incorporates market price
of volatility risk, and is generalizable to handle different kinds of
stochastic volatility models. We also demonstrate that with
historical data for two stocks, and appropriately chosen market price
of volatility risk, the algorithm yields option prices which are highly
consistent with market data.
Keywords: American option, pricing, stochastic volatility model, arbitrage, risk-neutral, dynamic programming, sequential, Monte Carlo, decision.
The manuscript is available in PDF format.