Valuation of European Options under an Uncertain Market Price of Volatility Risk (2105.09581v1)

Abstract: We propose a model to quantify the effect of parameter uncertainty on the option price in the Heston model. More precisely, we present a Hamilton-Jacobi-BeLLMan framework which allows us to evaluate best and worst case scenarios under an uncertain market price of volatility risk. For the numerical approximation the Hamilton--Jacobi--BeLLMan equation is reformulated to enable the solution with a finite element method. A case study with butterfly options exhibits how the dependence of Delta on the magnitude of the uncertainty is nonlinear and highly varied across the parameter regime. Keywords: Uncertain market price, Volatility risk, Hamilton-Jacobi-BeLLMan equation, Finite element method, Uncertainty quantification