Pricing Derivatives with Counterparty Risk and Collateralization: A Fixed Point Approach

European Journal of Operations Research, 2015, Forthcoming

28 Pages Posted: 16 Nov 2013 Last revised: 23 Jun 2015

See all articles by Jinbeom Kim

Jinbeom Kim

Barclays

Tim Leung

University of Washington - Department of Applied Math

Date Written: January 25, 2015

Abstract

This paper studies a valuation framework for financial contracts subject to reference and counterparty default risks with collateralization requirement. We propose a fixed point approach to analyze the mark-to-market contract value with counterparty risk provision, and show that it is a unique bounded and continuous fixed point via contraction mapping. This leads us to develop an accurate iterative numerical scheme for valuation. Specifically, we solve a sequence of linear inhomogeneous PDEs, whose solutions converge to the fixed point price function. We apply our methodology to compute the bid and ask prices for both defaultable equity and fixed-income derivatives, and illustrate the non-trivial effects of counterparty risk, collateralization ratio and liquidation convention on the bid-ask spreads.

Keywords: bilateral counterparty risk, collateralization, credit valuation adjustment, fixed point method, contraction mapping

JEL Classification: G12, G13, G23, C63

Suggested Citation

Kim, Jinbeom and Leung, Tim, Pricing Derivatives with Counterparty Risk and Collateralization: A Fixed Point Approach (January 25, 2015). European Journal of Operations Research, 2015, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2355177 or http://dx.doi.org/10.2139/ssrn.2355177

Jinbeom Kim (Contact Author)

Barclays ( email )

745 7th avenue, NY 10019
United States

Tim Leung

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

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