1 Derivatives Advanced Topics: Interest Rate

Transcript:1 Derivatives Advanced Topics: Interest Rate:
1 Derivatives Advanced Topics: Interest Rate Derivatives and Interest Rate Models Some of the most important and most actively used derivatives are those based on interest rates. These allow management of interest rate risk on loans and bonds. We first review how interest rate futures and forwards work and how to set up hedges with these contracts. We then go on to consider interest rate swaps and to extend the ideas from option valuation to interest rate derivative products with option features such as caps and floors. The most basic model for interest rate options is the Black model, a variant of Black-Scholes. Unfortunately, the empirical evidence shows that real world interest rate processes are considerably more complicated than simple logarithmic diffusions. We discuss the problems with the Black model framework and look briefly at alternative models of the interest rate process. As with other instruments, interest rate models come in both equilibrium and arbitrage-free formulations, with pros and cons attached to each. FINC-UB.0043, B40.3335 Futures and Options Spring 2019 Part III: Derivatives Advanced Topics ©2019 Figlewski 2 Interest Rate Derivatives and Interest Rate Models Important Concepts in this Section Types of interest rate derivatives Hedging with FRAs and Eurodollar futures Swaps The Black model for interest rate options How interest rate caps, floors, and collars work Problems with the Black model for pricing interest rate derivatives in the real world Alternative pricing models for interest-dependent securities equilibrium models (e.g., Vasicek model) arbitrage-free models (e.g., the LIBOR Market Model) FINC-UB.0043, B40.3335 Futures and Options Spring 2019 Part III: Derivatives Advanced Topics ©2019 Figlewski 3 Interest Rate Derivatives and Interest Rate Models Main Types of Interest Rate Derivatives The underlying is always an interest rate applied to a "notional" principal amount for a specified time period ("tenor"). The simplest interest rate derivatives are basic forward and option contracts, with a single maturity date. Forward Rate Agreement (FRA): A forward rate agreement is a kind of forward contract. A FRA fixes the interest rate to be paid on the notional principal at a specified strike value. The payment period (the tenor) begins on the contract's maturity date. If the market rate on that date is above the strike rate, the long FRA counterparty receives a payment from the short equal to the difference in interest cost between the two rates. If the market rate is lower than the strike rate, the long