Pricing collateralised options in the presence of counterparty credit risk: An extension of the Heston–Nandi model

Pierre J. Venter; Eben Maré

doi:10.37920/sasj.2022.56.1.3

Pierre J. Venter Department of Actuarial Science, University of Pretoria, South Africa; Department of Finance and Investment Management, University of Johannesburg, South Africa
Eben Maré Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa

DOI: https://doi.org/10.37920/sasj.2022.56.1.3

Keywords: Collateral, Counterparty credit risk, GARCH, Option pricing

Abstract

In this paper, a closed-formexpression for a collateralised European option in the presence of counterparty credit risk and stochastic volatility is derived. The model is applied to Standard and Poor’s 500 index options. The model prices obtained are consistent with expectations.