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The Whys of the LOIS: Credit Risk and Refinancing Rate Volatility

The 2007 subprime crisis has induced a persistent disconnection between the LIBOR derivative markets of dierent tenors and the OIS swap market. Commonly proposed explanations for the corresponding spreads are a combination of credit risk and liquidity risk. However in these explanations the meaning of liquidity in particular is either not precisely stated, or it is simply dened as a residual spread after removal of a credit component. In this paper we propose a stylized equilibrium model in which a LIBOROIS spread (LOIS) emerges as a consequence of a credit component determined by the skewness of the CDS curve of a representative borrower, and a liquidity component corresponding to the volatility of the cost-of-capital of a representative lender, where this cost-of-capital involves the lender’s CDS spread. The credit component is thus in fact a credit skewness component, and the relevant notion of liquidity appears as the optionality, valued by the aforementioned volatility, of dynamically adjusting through time the amount of a rolling OIS loan, as opposed to lending a xed amount up to the