Jaroszkowski, Bartosz;
Jensen, Max;
(2023)
Valuation of European Options Under an Uncertain Market Price of Volatility Risk.
Applied Mathematical Finance
, 29
(3)
pp. 213-226.
10.1080/1350486x.2022.2125884.
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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.
| Type: | Article |
|---|---|
| Title: | Valuation of European Options Under an Uncertain Market Price of Volatility Risk |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/1350486x.2022.2125884 |
| Publisher version: | https://doi.org/10.1080/1350486x.2022.2125884 |
| Language: | English |
| Additional information: | © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis GroupThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited. |
| Keywords: | Uncertain market price; volatility risk; Hamilton–Jacobi–Bellman equation; finite element method; uncertainty quantification |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10164364 |
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