Project CEMAPRE internal
|Title||Option pricing in Lévy models with transaction costs|
|Participants||Nicola Cantarutti, João Guerra (Principal Investigator), Manuel Guerra|
|Summary||Partial integro-differential equations (PIDE's) appear in option pricing models with jumps.|
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.
Our main goals are:
_develop a Markov chain approximation for the optimization problem related to the option pricing
problem in a exponential Lévy model market with transaction costs,
_prove the convergence of this Markov chain approximation and, if possible,
_prove the existence of a viscosity solution for the PIDE associated to this problem.