A Bayesian estimation of exponential Lévy models for implied volatility smile

Abstract

In this paper, a Bayesian estimation method for calibrating the parameter set of exponential Lévy models with the prior information and predicting distributions of option prices, is proposed. As real option prices are noisy, it is appropriate for option pricing models to provide confidence intervals for option prices. An algorithm for calibrating the parameter sets of exponential Lévy models is presented, and the performance of the proposed method is verified by comparing model-generated option prices with real market option prices such as KOSPI 200 Index option prices. Simulation results show that the proposed method calibrates the parameter sets effectively, overcoming the ill-posed inverse problem of model calibration and enabling the construction of reasonable predicted distributions of option prices.