Option Pricing and Calibration with Time-Changed Levy Processes

Abstract

Substantial empirical literature has suggested that the index dynamics should be free of diffusion components, which supports the importance of using infinite-activity jumps in option pricing problems. In this paper, a pure-jump stochastic volatility model is developed by using time-changed Levy processes. The proposed model distinguishes itself from existing time-change Levy models by incorporating the leverage effect and multi-scale volatility components. Due to the inexistence of explicit solution of European option prices, an efficient numerical algorithm known as the COS expansion is adopted. This numerical pricing framework can be applied to all time-changed Levy models, and the computation time is comparable to that of the traditional Carr-Madan FFT method. Calibration results based on real market data show that both long-run and short-run volatility components can be captured precisely with pure jump processes. The proposed model exhibits excellent performance, compared with several benchmark models, such as the celebrated Heston model.