Monte Carlo Greeks for European Pandemic Options under Stochastic SIS Model

Sammanfattning

This thesis investigates the numerical valuation of European pandemic options in a stochastic SIS model. The study focuses on whether non-standard features previously found in PDE-based analyses, including call price concavity and negative sensitivity to volatility, also arise in a Monte Carlo setting. The SIS process is discretised using the Euler--Maruyama method. This allows us to obtain explicit Monte Carlo pathwise sensitivity representations for the first two option sensitivities, Delta and Vega, which do not appear to be explicitly derived elsewhere in the literature. In contrast, the explicit pathwise sensitivity representation for the Gamma was unavailable since the payoff function at the strike has discontinuous second derivative. Therefore, it was approximated by the central finite--difference scheme. We conduct further numerical experimental study. The numerical results reproduce the main qualitative behaviour found in the literature. The call price is increasing but concave in the initial infection level, and the call Vega remains negative over the volatility grid considered. For the put option, the value decreases with the initial infection level and Vega is positive. Overall, the results indicate that these non-standard features arise naturally from the structure of the stochastic SIS model.