Derivatives: Markets, Valuation, and Risk Management

CHAPTER 4

No-Arbitrage Price Relations: Forwards, Futures, Swaps

In Chapter 1, we described the nature of exchange-traded and OTC derivatives contracts traded worldwide. Of these, the lion's share is plain-vanilla forwards, futures, and swaps. The purpose of this chapter is to develop no-arbitrage price relations for forward, futures, and swap contracts. In doing so, we rely only on the assumption that two perfect substitutes must have the same price. The two substitutes, in this case, are a forward/futures contract and a levered position in the underlying asset. The key to understanding the forward/futures valuation lies in identifying the net cost of carrying (i.e., “buying and holding”) an asset. We begin therefore with a discussion of carry costs/benefits. We then proceed by developing a number of important no-arbitrage relations governing forward and futures prices. Finally, we show that, since a swap contract is an exchange of future payments at a price agreed upon today, it can be valued as a portfolio of forward contracts. The chapter concludes with a brief summary.

UNDERSTANDING CARRY COSTS/BENEFITS

Derivative contracts are written on four types of assets—stocks, bonds, foreign currencies and commodities. The derivatives literature contains seemingly independent developments of derivative valuation principles for each type of asset. Generally speaking, however, the valuation principles are not asset-specific. The only distinction among assets is how carry costs/benefits ...