Pricing derivatives with counterparty risk and collateralization: A fixed point approach

Jinbeom Kim and Tim Leung

European Journal of Operational Research, 2016, vol. 249, issue 2, 525-539

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, (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (12)

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Working Paper: Pricing Derivatives with Counterparty Risk and Collateralization: A Fixed Point Approach (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:249:y:2016:i:2:p:525-539

DOI: 10.1016/j.ejor.2015.06.055

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