Pricing and hedging European-style options in Lévy-based stochastic volatility models considering the leverage effect

This paper develops a semi-analytical exact solution for the discrete-time variance-optimal hedging strategy based on two-dimensional Fourier cosine series expansions. This approach is novel and is more efficient than those previously suggested in the literature. Numerical studies for different models also suggest that the algorithm has better accuracy and stability for the pricing and hedging problems. A Lévy-based stochastic volatility model considering the leverage effect is also proposed. We have employed data on Apple stock prices and the corresponding option contracts to test this model to evaluate its ability to perform pricing and hedging. In summary, our model design is relatively reliable in the context of the known empirical patterns such as the existence of jumps, the volatility smile and the negative correlation between asset returns and volatilities.