Fixed Income Securities: Valuation, Risk, and Risk Management

CHAPTER 19

NO ARBITRAGE MODELS AND STANDARD DERIVATIVES

When a model is not able to fit exactly the term structure of interest rate, such as the Vasicek model in the relative value trade example in Chapter 16, Section 16.3, then it may imply two possibilities: (a) There is an arbitrage opportunity to be played on the term structure of interest rates; or (b) The model is flawed. Indeed, extensions to the Vasicek or the Cox, Ingersoll, and Ross models with multiple factors have been designed to indeed spot misalignment in the yields across maturities and therefore imply some type of (near) arbitrage strategy across yields. The model in this case is used to determined both the type of strategy to implement, as well as the hedge ratios and trading strategies. We discussed an example of these strategies in Section 16.3 of Chapter 16.

For many market participants, however, term structure models are designed to “simply” compute the fair value of many derivative securities, such as options, caps, floors, and swaptions. For these market participants it is important to fit the term structure of interest rates correctly, as we have done in Chapter 11 with trees. In this chapter, we review the most famous, and in fact most used models, of the term structure of interest rates, and their application to pricing standard derivatives, that is, plain vanilla options that are routinely used by financial institutions and end users to hedge interest rate risk.

19.1 NO ARBITRAGE MODELS

Why is it important ...