Research projects

Project CEMAPRE internal

TitleOption pricing in Lévy models and integro-differential equations
ParticipantsNicola Cantarutti, Manuel Guerra, João Guerra (Principal Investigator), Raúl Narciso
SummaryPartial 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.