Fixed Income Mathematics

Chapter 22: Futures Contracts

This chapter covers futures contracts and some of their mathematics. We start with a mention of cash contracts and a discussion of forward contracts, and we present several examples of how these are used. We then move to a discussion of future contracts and explain how they differ and how future contracts differ from forward contracts. We develop the equation for cost of carry and present and explain the equations for the conversion factors for Treasury security futures.

When you finish this chapter, you should understand the important features of cash, forward, and futures contracts, the cost to carry a future, and the conversion factors for Treasury futures.

CASH, FORWARD, AND FUTURES TRADES

When you buy a security in a normal trade, you expect to take delivery and pay for the security in the usual time, typically three business days from the trade date. This is called a cash transaction. For most individual investors, this is their most common investment transaction. Other types of purchase contracts exist, however.

Suppose you heat your house with oil, and in the summer your oil supplier offers you a deal. You agree to buy your oil, for delivery in the winter, at a price agreed upon now, in the summer. When winter arrives, your dealer will deliver the oil and charge you the price you agreed upon in summer. You agreed, in summer, to buy a product, the heating oil, at a future date, in winter, at a certain price, agreed upon in...

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