Derivatives Pricing Under Bilateral Counterparty Risk

31 Pages Posted: 17 Oct 2017

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.

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Date Written: September 14, 2017

Abstract

We consider risk-neutral valuation of a contingent claim under bilateral counterparty risk using the well-known reduced-form approach. Probabilistic valuation formulas derived under this framework cannot be used for practical pricing due to their recursive path dependencies. By imposing restrictions on the dynamics of the risk-free rate and stochastic intensities of counterparties’ default times, we develop path-independent probabilistic valuation formulas that have closed-form solutions or can lead to computationally efficient pricing schemes. Our framework also incorporates wrong-way risk (WWR). Advancing the work of Ghamami and Goldberg, we derive calibration- implied formulas that enable us to compare derivatives values in the presence and absence of WWR. We illustrate that derivatives values under WWR need not be less than derivatives values in the absence of WWR. A sufficient condition under which this inequality holds is when the price process follows a semimartingale with independent increments.

Keywords: Asset Pricing, Reduced-Form Modeling, Counterparty Risk, Wrong-Way Risk (WWR), Credit Value Adjustment (CVA)

Suggested Citation

Carr, Peter P. and Ghamami, Samim, Derivatives Pricing Under Bilateral Counterparty Risk (September 14, 2017). Journal of Risk, Forthcoming. Available at SSRN: https://ssrn.com/abstract=3054435

Peter P. Carr (Contact Author)

New York University Finance and Risk Engineering ( email )

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

Samim Ghamami

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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