Representations for conditional expectations and applications to pricing and hedging of financial products in Lévy and jump-diffusion setting
In this paper, we derive expressions for conditional expectations in terms of regular expectations without conditioning but involving some weights. For this purpose we apply two approaches: the conditional density method and the Malliavin method. We use these expressions for the numerical estimation of the price of American options and their deltas in a Lévy and jump-diffusion setting. Several examples of applications to financial and energy markets are given including numerical examples.
Conditional expectation, Monte Carlo methods, Conditional density method, Malliavin calculus, Pricing, Lévy processes, American option, Reduction of variance