CVA, FVA (and DVA?) with stochastic spreads. A feasible replication approach under realistic assumptions.

García Muñoz, Luis Manuel (2013): CVA, FVA (and DVA?) with stochastic spreads. A feasible replication approach under realistic assumptions.

Abstract

In this paper we explore the different components that should be incorporated in the price of uncollateralized derivatives. We do so by putting special focus on the hedge-ability of every term. In order to reflect the most realistic situation, we assume stochastic credit spreads for both counterparties. In such a framework, the counterparty acting as the hedger will be concerned about market risk (movements in the price of the underlying asset), both sources of the credit risk of the investor (spread changes and default event) and also his own credit risk. Regarding his own credit risk, we assume that the derivatives hedger has no incentive to hedge the change in value of the derivative upon his own default, since the hedger will not be exposed to this change in value. Nevertheless, we assume that the hedger has a strong incentive to hedge the changes in the derivative’s price due to changes in his credit spread curve, which is a source of risk that the derivatives hedger will be exposed to during the replication process. We also suggest a hedging strategy for this risk factor (spread changes of the investor) as we do for the other (market risk, spread changes and default event of the issuer). We conclude that under these assumptions CVA (a unilateral version of it that does not depend on the hedger’s funding curve) and FVA (a funding adjustment that does only depend on the investor’s default indicator and not on the hedger’s) are the only components to be incorporated in the price of financial derivatives.

• Item Type: MPRA Paper
• Language: English
• Keywords: CVA; DVA; FVA; Collateral; Full replication
• Subjects: G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G10 - General; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing

References

D. Brigo, A. Pallavicini and D. Perini. Funding, Collateral and Hedging: Uncovering the Mechanics and the Subtleties of Funding Valuation Adjustments. http://papers.ssrn.com/sol3/papers.cfm?abstract id=2161528, October, 2012.

C. Burgard and M. Kjaer. Partial differential equation representations of derivatives with counterparty risk and funding costs. The Journal of Credit Risk, Vol. 7, No. 3, 1-19, 2011.

C. Burgard, M. Kjaer. In the balance, Risk, Vol 11, 72-75, 2011.

C. Burgard, M. Kjaer. Generalised CVA with funding and collateral via semi-replication, Working paper. Dec 2012. http://papers.ssrn.com/sol3/papers.cfm?abstract id=2027195

A. Castagna. On the Dynamic Replication of the DVA: Do Banks Hedge their Debit Value Adjustment or their Destroying Value Adjustment?. July, 2012. http://www.iasonltd.com/FileUpload/files/DVA%20Dynamic%20Replication.pdf

A. Castagna. Funding, liquidity, credit and counterparty risk: Links and implications. Iason research paper. http://iasonltd.com/resources.php, 2011.

J. Gregory. Being Two-faced over Counterpartyrisk. Risk, February, 2009.

J. Gregory. Counterparty credit risk and credit value adjustment. Wiley, 2nd edition, 2012.

J. Hull, A. White. The FVA debate, Risk, Aug 2012.

J. Hull, A. White. The FVA debate continued, Working paper, Sep 2012.

J. Hull, A. White. CVA, DVA, FVA and the Black-Scholes-Merton Arguments, Working paper, Sep 2012.

M. Kjaer. A generalized credit value adjustment. The Journal of Credit Risk, Vol. 7, No. 1, 1-28, 2011.

M. Morini and A. Pramploni. Risky funding with counterparty and liquidity charges. Risk, March, 70-75, 2011.

V. Piterbarg. Funding beyond discounting: Collateral agreements and derivatives pricing. Risk, February, 97-102, 2010.

V. Piterbarg. Cooking with collateral. Risk, August, 2012.