A Second Look at Post Crisis Pricing of Derivatives - Part I: A Note on Money Accounts and Collateral

Hovik Tumasyan

MPRA Paper from University Library of Munich, Germany

Abstract: The paper reviews origins of the approach to pricing derivatives post-crisis by following three papers that have received wide acceptance from practitioners as the theoretical foundations for it - [Piterbarg 2010], [Burgard and Kjaer 2010] and [Burgard and Kjaer 2013]. The review reveals several conceptual and technical inconsistencies with the approaches taken in these papers. In particular, a key component of the approach - prescription of cost components to a risk-free money account, generates derivative prices that are not cleared by the markets that trade the derivative and its underlying securities. It also introduces several risk-free positions (accounts) that accrue at persistently non-zero spreads with respect to each other and the risk free rate. In the case of derivatives with counterparty default risk [Burgard and Kjaer 2013] introduces an approach referred to as semi-replication, which through the choice of cost components in the money account results in derivative prices that carry arbitrage opportunities in the form of holding portfolio of counterparty's bonds versus a derivative position with it. This paper derives no-arbitrage expressions for default-risky derivative contracts with and without collateral, avoiding these inconsistencies. It will be followed by a part two paper that deals with the derivation of XVA expressions based on the approach in this paper.

Keywords: Financial crisis; collateral; derivatives; XVA; no-arbitrage pricing; counterparty default (search for similar items in EconPapers)
JEL-codes: G01 G10 G12 G13 G19 G21 (search for similar items in EconPapers)
Date: 2018-12-23
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