Fixed Income Analysis, Second Edition

CHAPTER 14

VALUATION OF INTEREST RATE DERIVATIVE INSTRUMENTS

I. INTRODUCTION

In the previous chapter, we described interest rate derivative instruments—futures, forwards, options, swaps, caps, and floors. In this chapter, we focus on the valuation of these instruments. Later, we will see how they can be used by portfolio managers to control interest rate risk.

II. INTEREST RATE FUTURES CONTRACTS

In this section we will use an illustration to show how a futures contract is valued. Suppose that a 20-year, $100 par value bond with a coupon rate of 8% is selling at par and that the next coupon payment is six months from now. Also suppose that this bond is the deliverable for a futures contract that settles in three months. If the current 3-month interest rate at which funds can be loaned or borrowed is 4% per year, what should be the price of this futures contract?

Suppose the price of the futures contract is 105. Consider the following strategy:

Sell the futures contract that settles in three months at $105.

Borrow $100 for three months at 4% per year.

With the borrowed funds, purchase the underlying bond for the futures contract.

This strategy is shown in Exhibit 1.

Notice that, ignoring initial margin and other transaction costs, there is no cash outlay for this strategy because the borrowed funds are used to purchase the bond. Three months from now, the following must be done:

Deliver the purchased bond to settle the futures contract.

Repay the loan.

When the bond is delivered ...