Mathematical Finance Seminar
RUD 25, 1.113
Christoph Belak

Option Pricing under Jump Uncertainty

We study the problem of European and American option pricing in the presence of uncertainty about the timing and the size of a jump in the price of the underlying. In a non-Markovian market setting, we characterize the worst-case option price as the minimal solution of a constrained backward stochastic differential equation and derive a pricing PDE in the special case of a Markovian market model. In a Black-Scholes market, explicit pricing formulae for European call and put options are obtained, and we study properties of the American put option price numerically.