Pricing, Hedging and Assessing Risk in a General Lévy Context

The goal of this paper is to suggest a general approach for risk management by allowing jumps to occur in the underlying of a European contingent claim. It gives a unified methodology for pricing, hedging and computing the standard risk measures, namely the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). The core of the paper shows that such quantities as prices, hedging ratios and standard risk measures can be expressed as an integral form articularly suited for the calculation by FFT, simply by changing the integrand. The method can be applied as soon as the characteristic exponent of the Lévy rocess is known. The suggested unified method is easier to implement than the numerical solution to PIDE and faster than Monte Carlo simulations. It gives a powerful tool to practitioners who want to price and control risk of European derivatives in a non-Gaussian setting.