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

67 Pages Posted: 13 Aug 2014

See all articles by Robert Huitema

Robert Huitema

University of Zurich - Department of Banking and Finance

Bas Peeters

Vrije Universiteit Amsterdam, School of Business and Economics

Date Written: August 12, 2014

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.

Keywords: Stochastic volatility, jump-diffusion modeling, risk aversion, market modeling, implied volatility surface

JEL Classification: C11, C13, C32, G11, G13, G17

Suggested Citation

Huitema, Robert and Peeters, Bas, Risk Premiums in a Multi-Factor Jump-Diffusion Model for the Joint Dynamics of Equity Options and Their Underlying (August 12, 2014). Available at SSRN: https://ssrn.com/abstract=2479597 or http://dx.doi.org/10.2139/ssrn.2479597

Robert Huitema (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Sch├Ânberggasse 1
Z├╝rich, 8001
Switzerland

Bas Peeters

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

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