Derivatives Pricing Under Bilateral Counterparty Risk

28 Pages Posted: 3 Apr 2015 Last revised: 12 Apr 2015

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Samim Ghamami

University of California, Berkeley - Center for Risk Management Research; New York University (NYU); Goldman Sachs Group, Inc.

Date Written: April 12, 2015

Abstract

We consider risk-neutral valuation of a contingent claim under bilateral counterparty risk in a reduced-form setting similar to that of Duffie and Huang [1996] and Duffie and Singleton [1999]. The probabilistic valuation formulas derived under this framework cannot be usually used for practical pricing due to their recursive path-dependencies. Instead, finite-difference methods are used to solve the quasi-linear partial differential equations that equivalently represent the claim value function. By imposing restrictions on the dynamics of the risk-free rate and the stochastic intensities of the counterparties' default times, we develop path-independent probabilistic valuation formulas that have closed-form solution or can lead to computationally efficient pricing schemes. Our framework incorporates the so-called wrong way risk (WWR) as the two counterparty default intensities can depend on the derivatives values. Inspired by the work of Ghamami and Goldberg [2014] on the impact of WWR on credit value adjustment (CVA), we derive calibration-implied formulas that enable us to mathematically compare the derivatives values in the presence and absence of WWR. We illustrate that derivatives values under unilateral WWR need not be less than the derivatives values in the absence of WWR. A sufficient condition under which this inequality holds is that the price process follows a semimartingale with independent increments.

Keywords: Reduced-Form Modeling, Counterparty Risk, Wrong Way Risk, Credit Value Adjustment, Basel III

JEL Classification: G12, G2, C63

Suggested Citation

Carr, Peter P. and Ghamami, Samim, Derivatives Pricing Under Bilateral Counterparty Risk (April 12, 2015). Available at SSRN: https://ssrn.com/abstract=2588487 or http://dx.doi.org/10.2139/ssrn.2588487

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Samim Ghamami (Contact Author)

University of California, Berkeley - Center for Risk Management Research ( email )

581 Evans Hall
Berkely, CA 94720
United States

New York University (NYU) ( email )

Bobst Library, E-resource Acquisitions
20 Cooper Square 3rd Floor
New York, NY 10003-711
United States

Goldman Sachs Group, Inc. ( email )

85 Broad Street
New York, NY 10004
United States

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