Valuation of European Options under an Uncertain Market Price of Volatility Risk

2021/05/20 by Bartosz Jaroszkowski, Max Jensen, Jaroszkowski, Bartosz +1
Economics, Econometrics and Finance · #Stochastic processes and financial applications #Capital Investment and Risk Analysis

paper · pdf · doi:10.48550/arxiv.2105.09581

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

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