Empirical Performance of Models for Valuation and Risk-Management of Barrier Options

Abstract

In this paper the empirical performance of alternative models for barrier option valuation and risk management is studied. Five commonly used models are compared: the Black-Scholes model, the constant elasticity of variance model, the Heston stochastic volatility model, the Merton jump-diffusion model, and the infinite activity Variance Gamma model. We employ time-series data from the USD/EUR exchange rate market, and use plain vanilla option prices as well as a unique data-set of observed market values of barrier options. The different models are calibrated to the plain vanilla option prices, and cross-sectional and predicted pricing errors for both plain vanilla and barrier options are investigated. For the plain vanilla options the Heston model has superior performance both in cross-section and for prediction horizons of up to one month, with its closest competitors being the Merton and the Variance Gamma models. For the barrier options, the Heston model has a slightly, but not significantly, better performance than the continuous alternatives Black-Scholes and constant elasticity of variance, while both models with jumps(Merton and Variance Gamma) perform markedly worse.