On the Determination of the Lévy Exponent in Asset Pricing Models

We consider the problem of determining the Lévy exponent in a geometric Lévy model for asset prices, given the price data of derivatives. The model, formulated under the real-world probability measure, consists of a pricing... [ view full abstract ]

We consider the problem of determining the Lévy exponent in a geometric Lévy model for asset prices, given the price data of derivatives. The model, formulated under the real-world probability measure, consists of a pricing kernel together with one or more risky assets driven by the same Lévy process. We show that if the prices of power-payoff derivatives, for which the payoff is the value of the benchmark portfolio raised to the power q, are given for a range of values of q,  then the Lévy exponent is completely determined up to an irrelevant linear additive factor.