Fast Valuation of Options Under Parameter Uncertainty

Abstract:
Option valuation is typically done under the assumption of perfect knowledge about latent states (such as stochastic volatility) and parameters, an assumption that is rather dubious from a statistical point of view! This needs to be accounted for without introducing arbitrage.



Fourier based methods for computing (vanilla) option values are nowadays the bread and butter in many risk management systems in the financial industry. We introduce a correction for the (parameter and state) uncertainty that previously had to be computed using Monte Carlo methods or deterministic quadrature into the Fourier based framework.



We find that these new Fourier methods are retaining all the good properties we have gotten used to, being fast, accurate and applicable to a wide range of models.