Risk Premiums in a Multi-Factor Jump-Diffusion Model for the Joint Dynamics of Equity Options and Their Underlying

Abstract

This paper proposes a new approach to measure premiums for volatility and jump risks in option markets. These risks are captured by a multi-factor jump-diffusion model for the joint evolution of the underlying and the implied volatility surface. This market-based approach enables us to carefully test and select the most relevant risk factors in option markets. We extend the approach of Schonbucher (1998) to processes that include jumps and derive a condition that ensures absence of dynamic arbitrage. As this condition is derived under the physical measure, it incorporates a premium for each risk factor in the model. We then interpret the no-arbitrage constraint as a noisy measurement of these risk premiums and other latent variables such as the volatility and jump-intensity of the underlying. This allows us to dynamically calibrate these variables to data from several markets using a Bayesian filtering framework. The results shed new light on how option risk premiums vary over time and across markets. As our approach provides an accurate and arbitrage-free description of option price dynamics it can also be used for risk management of portfolios of options and for testing dynamic option strategies.