Hedging options in the incomplete market with stochastic volatility

We show that it is possible to avoid the discrepancies of continuous path models for stock prices and still be able to hedge options if one models the stock price process as a birth and death process. One needs the stock and another market traded derivative to hedge an option in this setting. However, unlike in continuous models, the number of extra traded derivatives required for hedging does not increase when the intensity process is stochastic. We obtain parameter estimates using Generalized Method of Moments and describe the Monte Carlo algorithm to obtain option prices. We show that one needs to use filtering equations for inference in the stochastic intensity setting. We present real data applications to study the performance of our modeling and estimation techniques.

Keywords

birth and death process, Bayesian filtering, edgeworth expansion, convergence of stochastic processes, generalized method of moments, Monte Carlo algorithm, hidden Markov model

2010 Mathematics Subject Classification

60F05, 60G44, 62M20, 62P05

Full Text (PDF format)

Published 1 January 2009