Underlying the standard methods of pricing derivative contracts is the assumption that market participants can borrow and lend in unlimited amounts at the risk-free rate. The most frequently traded interest rate derivatives have payoffs that depend on the inter-bank borrowing rate (LIBOR). Traditionally, the pricing and risk management of these interest rate derivatives have assumed that this rate is ‘risk-free’.
Since the advent of the financial crisis that began in 2007, these assumptions have been violated to a considerable degree. In this work, we explore the implications of this for the relative valuation of simple interest-rate derivative contracts that depend on interbank lending rates.
This paper is organized as follows. We begin by providing more detail about the theoretical context of this study and its relationship to previous literature. Next, we present intuitive arguments that illustrate how credit risk and illiquidity leads to the breakdown of basic relationships among different forward rates. We document that these relationships held until the start of the credit crisis in August 2007, but were then subsequently violated, leading to relative mispricings of interest rate derivative contracts. We shall refer to these mispricings as ‘anomalies’.
We perform an empirical regression analysis, illustrating how these anomalies depend on market variables. To assess whether bid-ask spreads can explain the size of the mispricings, we examine market data for interbank loans traded on an exchange. We then introduce more formal models of credit and liquidity risk that can explain these mispricings, and show how these models imply differences in the behavior of the term structure of these pricing anomalies.
Derivative agreements are priced by appealing to arguments based on the absence of arbitrage. Assume that two parties engage in a derivative transaction, i.e. a contract that depends on the value of an underlying asset, such as a stock or bond. Both parties can then hedge the impact of this derivative through a strategy that entails buying or selling other derivatives or the underlying asset. If the hedge is perfect, the market risk incurred by taking on the derivative position is eliminated. The hedged portfolio, by absence of arbitrage, should have a return equal to the risk-free rate. This constraint enforces a relationship between the values of the derivative and the instruments that are used as a hedge.
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Interest Rate Derivative Pricing when Banks are Risky and Markets are Illiquid
