American Option Valuation with Particle Filters

A method to price American-style option contracts in a limited information framework is introduced. The pricing methodology is based on sequential Monte Carlo techniques, as presented in Doucet, de Freitas, and Gordon's text "Sequential Monte Carlo Methods in Practice", and the least-squares Monte Carlo approach of Longstaff and Schwartz [The Review of Financial Studies, 14 (2001), 113–147]. We apply this methodology using a risk-neutralized version of the square-root mean-reverting model, as used for European option valuation by Heston [The Review of Financial Studies, 6 (1993), 327–343]. We assume that volatility is a latent stochastic process, and we capture information about it using particle filter based "summary vectors." These summaries are used in the exercise/hold decision at each time step in the option contract period. We also benchmark our pricing approximation against the full-state (observable volatility) result. Moreover, posterior inference, utilizing market-observed American put option prices on the NYSE Arca Oil Index, is made on the volatility risk premium, which we assume is a constant parameter. Comparisons on the volatility risk premium are also made in terms of time and observability effects, and statistically significant differences are reported