Pricing European call options with interval-valued volatility and interest rate

Song Wang

Applied Mathematics and Computation, 2024, vol. 474, issue C

Abstract: We propose a novel approach to pricing European call options when both of the volatility of the underlying asset and interest are uncertain. In this approach, we formulate the option pricing problem with uncertain parameters as a partial-differential inequality constrained interval optimization problem. An interior penalty method is then developed for the numerical solution of the finite-dimensional optimization problem arising from the discretization of the continuous pricing problem by a finite difference scheme. A convergence theory for the penalty method is established. An algorithm based on Newton's iterative method is also proposed for solving the penalty equation. Numerical results are presented to demonstrate the effectiveness and usefulness of this approach and the numerical methods.

Keywords: Interval optimization; Partial-differential inequality constrained optimization; European call option valuation under uncertainties; Variational inequality; Interior penalty method; Finite differences (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:474:y:2024:i:c:s009630032400170x

DOI: 10.1016/j.amc.2024.128698

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