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

Bartosz Jaroszkowski and Max Jensen

Applied Mathematical Finance, 2022, vol. 29, issue 3, 213-226

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.

Date: 2022
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DOI: 10.1080/1350486X.2022.2125884

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