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

Tumasyan, Hovik (2018): A Second Look at Post Crisis Pricing of Derivatives - Part I: A Note on Money Accounts and Collateral.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Financial crisis, collateral, derivatives, XVA, no-arbitrage pricing, counterparty default
• Subjects: G - Financial Economics > G0 - General > G01 - Financial Crises; G - Financial Economics > G1 - General Financial Markets > G10 - General; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing; G - Financial Economics > G1 - General Financial Markets > G19 - Other; G - Financial Economics > G2 - Financial Institutions and Services > G21 - Banks ; Depository Institutions ; Micro Finance Institutions ; Mortgages

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Tumasyan, Hovik, A Second Look at Pricing Derivatives Post Crisis - Part II: XVAs and Balance Sheet Consumption, forthcoming