Empirical Performance of Models for Barrier Option Valuation

In this paper the empirical performance of ve di erent models for barrier op- tion valuation is investigated: the Black-Scholes model, the constant elasticity of variance model, the Heston stochastic volatility model, the Merton jump-di usion model, and the in nite activity Variance Gamma model. We use time-series data from the USD/EUR exchange rate market: standard put and call (plain vanilla) option prices and a unique set of observed market values of barrier options. The models are calibrated to plain vanilla option prices, and prediction errors at dif- ferent horizons for plain vanilla and barrier option values are investigated. For plain vanilla options, the Heston and Merton models have similar and superior performance for prediction horizons up to one week. For barrier options, the continuous-path models (Black-Scholes, constant elasticity of variance, and Hes- ton) do almost equally well, while both models with jumps (Merton and Variance Gamma) perform markedly worse