Collateral choice and the fundamental theorem of asset pricing

García Muñoz Luis Manuel

MPRA Paper from University Library of Munich, Germany

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.

Keywords: fundamental theorem of asset pricing; collateral; change of numeraire; Radon Nikodym derivative; martingale measure (search for similar items in EconPapers)
JEL-codes: G10 G12 G13 (search for similar items in EconPapers)
Date: 2012-10-09
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