Abstracts

Empirical evidence has shown that some Lévy processes provide a better model fit for market option prices compared with the traditional Black-Scholes models. Greeks are price sensitivities of financial derivatives and are essential for hedging and risk management. But to calculate the Greeks under Lévy process is a challenging and timely task. To overcome this difficulty, this paper proposes a direct method for calculating the Greeks. Briefly speaking, our proposed method provides a ``differentiation' of an indicator function, so that the product rule and chain rule remain valid once the order of the integration and differentiation is switched. Explicit examples for calculating deltas, vegas, and gammas of European and Asian options under Merton's model and the variance-gamma process are given. Numerical results confirm that the proposed method outperforms existing methods, in terms of unbiasedness, efficiency, and computational time.