Sequential Monte Carlo for Early-Exercise Option Pricing

Stochastic Analysis Seminar Series

A review of a valuation strategy to price American-style option contracts in a “limited information” framework is discussed where sequential Monte Carlo (SMC) techniques, as presented in Doucet, de Freitas, and Gordon’s text Sequential Monte Carlo Methods in Practice, and the least–squares Monte Carlo (LSM) approach of Longstaff and Schwartz (Review of Financial Studies 14:113-147, 2001), are used as part of the valuation methodology. We utilize a risk–neutralized version of a mean-reverting model to model the volatility process. We assume that volatility is a latent stochastic process, and we capture information about it using “summary vectors” based on sequential Monte Carlo posterior filtering distributions. Of primary interest in this work is an empirical assessment of American options governed by a stochastic volatility model where the focus is on the market price of volatility risk (or the volatility risk premium). We discuss statistical modeling of the market price of volatility risk as our current evidence reveals interesting nuances about the volatility risk premium, and we hypothesize that switching models or more sophisticated time-series models could be of value to understand the empirical observations we found on the market price of volatility risk. Prior studies have shown that the magnitude of the volatility risk premium changes markedly when an American index option (NYSE Arca Oil Index Options) is in its expiration month relative to prior months, or that the magnitude varies across equities. Our objective is to study if useful information can be extracted from the volatility risk premium process, and how this information can better inform holders of American options when making decisions under uncertainty.

Key words: American options, stochastic volatility, volatility risk, sequential, Monte Carlo, risk premium, decisions, uncertainty

Disclaimer: The views expressed in this abstract (and the paper that will accompany it) are solely those of the authors and do not, in any way, reflect the opinions of the Office of the Comptroller of the Currency (OCC).






Monday, November 11, 2013 - 14:15
to 15:15