Fixed Income Securities: Valuation, Risk, and Risk Management

CHAPTER 15

NO ARBITRAGE AND THE PRICING OF INTEREST RATE SECURITIES

In this chapter we illustrate the key steps in the derivation of prices of interest rate securities, including Treasury bonds and derivative instruments. The key is to impose the understanding that financial markets do not leave arbitrage opportunities available for arbitrageurs. Why is this approach useful? It provides constraints that have to be satisfied if there are no arbitrage opportunities left on the table. Sometimes frictions prevent market prices from moving in a way to eliminate arbitrage opportunities, and thus an arbitrageur can step in, set up a trade, and make arbitrage profits. The way an arbitrageur can detect the presence of an arbitrage opportunity is by checking the difference between market prices and the ones dictated by no arbitrage rules. If the discrepancy is large, it means that an arbitrage is potentially feasible. Of course, this procedure is based on the arbitrageur’s faith in his or her own model used to detect the presence of the arbitrage opportunity. That is to say, what could be deemed an arbitrage opportunity in one model may not be an arbitrage opportunity according to another model. Because reality is much more complex than what a model can describe, models provide guidance in setting up arbitrage strategies, but some error margin may still exist.

Even so, using a model to decide the feasibility of an arbitrage trade is a key step. A model determines the feasibility of a trade ...