Project CEMAPRE internal
| Title | Option pricing in Lévy models and integro-differential equations |
| Participants | Nicola Cantarutti, João Guerra (Principal Investigator), Manuel Guerra, Raúl Narciso |
| Summary | Partial integro-differential equations (PIDE's) appear in option pricing with discontinuous models. These equations generalize the Black-Scholes PDE when the continuous diffusion dynamics for the underlying price is replaced by a Lévy process dynamics (including jumps). The integral operator in the PIDE propagates a possible irregularity of the solution. For many exponential Lévy models (such as Variance Gamma) or for Barrier options, the option price may not be sufficiently regular. This drawback led several authors to consider option prices as weak solutions (viscosity solutions) of the PIDEs. Our main goals are: (i) to obtain sufficient conditions for the existence of a viscosity solution for the PIDE associated to the option pricing problem in a exponential Lévy model market with transaction costs; (ii) develop numerical schemes based on finite differences and finite element methods for pricing PIDE's in general exponential Lévy models. |