Collateral choice and the fundamental theorem of asset pricing

Luis Manuel, García Muñoz (2012): Collateral choice and the fundamental theorem of asset pricing.

Abstract

In the classical quantitative finance literature it is assumed that there is a risk free rate at which hedgers can borrow and lend in the dynamic replication process of financial derivatives. In such a framework, under complete market conditions and absence of arbitrage opportunities, for a given numeraire whose price cannot vanish, prices of self financing portfolios divided by the numeraire behave like a martingales under a unique martingale measure associated with the numeraire. Nevertheless, in the current market environment a high percentage of deals are collateralized due to counperparty credit risk concerns. Depending on the collateral agreement, collateral can be in the form of cash in different currencies, but also in the form of assets (bonds, shares,...). In this paper we explore how the fundamental valuation theorem and the change of numeraire tollkit is reformulated under this new framework.

• Item Type: MPRA Paper
• Language: English
• Keywords: fundamental theorem of asset pricing; collateral; change of numeraire; Radon Nikodym derivative; martingale measure
• 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

Vladimir Piterbarg, Funding Beyond Discounting. Collateral agreements and derivatives pricing. Risk February 2010.

Fujii M and A Takahashi, Choice of collateral currency. Risk January 2011.

Vladimir Piterbarg, Cooking with collateral. Risk August 2012.