Option pricing in a jump-diffusion
model with large investor
Anna Lisa Amadori - Università di Roma La Sapienza
The aim of this work is to price by arbitrage contingent claims on an
underlying asset with discontinuous path (modelized by a
jump-diffusion process), in a market where the interest rate is influenced
by agents' trading policy.
The jump-diffusion model allows for discontinuous changes in prices as a
consequence of external events like instability of
exchange rate with foreign currencies, sudden changes in demand or offer
of commodities, big factories' policy.
On the other hand, it gives rise to a not complet market: we chose to add
a new asset in order to grant completeness.
Besides, the large investor model introduces nonlinear effects which may
be successfully treated by means of P.D.E.~approach.
We give a formal derivation of the integro-differential deterministic
operator related with the price of contingent claims.
Existence and uniqueness of viscosity solution for the final value
problem realated with European option is obtained through
Perron's method, via a comparison result. A penalization method gives
similar results for the obstacle problem, related with
American option. Some regularity results are given in both cases by means
of an adaptation of the comparison principle.