Empirical performance of models for barrier option valuation

Abstract

In this paper the empirical performance of five different models for barrier option valuation is investigated: 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 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 different 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 Heston) do almost equally well, while both models with jumps (Merton and Variance Gamma) perform markedly worse.JEL classification: G13 Keywords: Barrier option valuation, empirical performance. * We are deeply indebted to Morten Nalholm for his help cleaning and organizing the barrier option data, and to Fiodar Kilin for his help calibrating the Bates and VG-CIR models. We also thank three referees for valuable comments.

A mixed Monte Carlo and partial differential equation variance reduction method for foreign exchange options under the Heston–Cox–Ingersoll–Ross model

“…The calibrated Heston parameters. Column 2: for USD/EUR market data of 2 January 2004 -27 September 2005(Jessen and Poulsen 2013). Column 3: for EUR/USD market data of 22 August 2006(Elices and Giménez 2013).…”

Calibrating Option Pricing Models with Heuristics

“…(Unfortunately, different calibration criteria lead to different results, see Detlefsen and Härdle, 2007). In the same vein, Jessen and Poulsen (2009) find that different models, when calibrated to plain vanilla options, exhibit widely-differing pricing performance when used to explain actual prices of barrier options. Our results suggest that the lowly numerical optimisation itself can make a difference.…”

Hedging Barrier Options in GARCH Models with Transaction Costs

“…The data on barrier option prices covering the period 2 January 2004 to 27 September 2005 come from the risk‐management department of Danske Bank and a detailed description of the data set can be found in Jessen & Poulsen (). We considered only UOC barrier options and excluded options with values lower than in our evaluation of the hedging performance.…”