Hedging: Comparing the Alternatives
USD/EUR USD/EUR Cash-Flow
Alternative Increases Decreases Uncertainty Cost
Do nothing Gain Lose Maximal 0
Futures Lose Gain Minimal 0
Options Gain Protected Intermediate +ve
• In the futures contract, the high spot exchange rate hurts (we cannot take advantage of it because the delivery price is locked-in); however, the low spot exchange rate leaves us off for having locked in a higher rate.
Table 1.5 summarizes this comparison. The key point that emerges here is that there is no outcome that is dominant, i.e., that is better in all circumstances. Doing nothing is sometimes better than using futures or options but sometimes not. (In a sense, doing nothing is akin to betting on a favorable movement in prices, in this case, on the USD/EUR rate increasing. Like all speculation, this bet can go wrong.) Using futures provides cash-flow control, but the ex post outcome may not always look good. For instance, if the exchange rate moves to $1.0728/euro, the company is worse off for having hedged using futures—and it is useful to keep in mind here that regardless of our ex ante intentions, we are almost always judged in this world on ex post outcomes. Using options provides protection but involves a substantial up-front cost that may not be recouped by the gains from exercising the option—and that is fully lost if the option lapses unexercised.
Derivatives in Speculation
The preceding example dealt with hedging: the reduction of cash-flow uncertainty from a prior market commitment. Derivative securities can also be used to speculate i.e., to make profits by taking views on market direction.
Suppose, for example, that an investor believes that the Japanese yen (JPY) will appreciate significantly with respect to the US dollar (USD) over the next three months. The investor can speculate on this belief using derivatives in at least two ways:
1. By taking a long position in JPY futures deliverable in three months. 2. By buying a call option on JPY with an expiry date in three months.
(There is also the third alternative of buying the JPY in the spot market today and holding it for three months, but this strategy does not involve the use of derivatives.) In both cases, the investor makes money if his belief is vindicated, and the yen appreciates as expected. With the futures contract, the investor has locked-in a price for the future purchase of yen; any increase in price of yen over this locked-in rate results in a profit. With the call option, the investor has the right to buy yen at a fixed price, viz., the strike price in the contract. Any increase in the price of yen above this strike results in exercise-time profits for the investor. However, there are costs to both strategies. In the case of the futures, the cost is that the anticipated appreciation may fail to be realized; if the price of JPY instead falls, the futures contract leads to a loss, since it obligates the investor to buy yen at the higher locked-in price. In the case of options, the up-front premium paid is lost if the yen depreciates and the option lapses unexercised; but even if the option is exercised, the profits at exercise time may not be sufficient to make up the cost of the premium. Thus, once again, there is no one “best” way to use derivatives to exploit a market view.
1.5
The Structure of this Book
The main body of this book is divided into five (unequal) parts with a sixth technical part supplementing the material.
Part 1 of the book (Chapters 2–6) deals with futures and forwards. Chapter 2 discusses
futures markets and their institutional features. Chapters 3 and 4 deal with the pricing of futures and forward contracts. Chapter 3 develops the pricing theory, while Chapter 4 looks at the empirical performance of the theory and discuses extensions of the basic theory. Chapter 5 is concerned with hedging strategies in futures and forward markets, in particular the development and implementation of minimum-variance hedging strategies in situations in which a perfect hedge is impossible because of a mismatch between the risk being hedged and the available futures or forward contracts. Chapter 6 looks at a special class of futures and forward contracts—those defined on interest rates or bond prices, a category that includes some of the most successful contracts ever introduced, including eurodollar futures and Treasury futures.
Part 2, which deals mainly with options, is the longest segment of the book, comprising
Chapters 7–22. Chapters 7 and 8 cover preliminary material, including the role of volatility and a discussion of commonly used “trading strategies.” Chapters 9–16 are concerned with option pricing, beginning with no-arbitrage restrictions on these prices (Chapter 9) and put-call parity and related results (Chapter 10). Chapter 11 then provides a gentle introduction to option pricing and its key concepts (such as the option delta and risk-neutral pricing). Building on this foundation, Chapters 12 and 13 develop the binomial model of option pricing, while Chapters 14 and 15 present the Black-Scholes model. Chapter 16 discusses several generalizations of the basic binomial/Black-Scholes approach including jump-diffusions, stochastic volatility/GARCH-based models, and local volatility models.
Moving from pricing to the management of option risk, Chapter 17 looks at the “option greeks,” measures of option sensitivity to changes in market conditions. Chapters 18 and 19 move this discussion beyond the realm of plain vanilla options. Chapter 18 examines a range of “path-independent” exotic options, while Chapter 19 studies “path-dependent” exotics.
The remainder of Part 2 looks at special topics. The measurement of portfolio risk and the concepts of Value-at-Risk (or VaR) and risk-budgeting are introduced in Chapter 20. Convert- ible bonds and their pricing and hedging are the subject of Chapter 21. Finally, Chapter 22 examines the field of “real options,” optionalities embedded within investment projects.
Part 3 of the book (Chapters 23–25) examines swaps. Chapter 23 looks at interest rate
swaps, which constitute the great bulk of the swaps market. The workhorse of the interest rate swap market, the plain vanilla fixed-for-floating swap, is examined in detail, as are several others. This chapter also introduces caps, floors, and swaptions, and presents the so-called “market model” commonly used to value these instruments. Chapter 24 moves on to equity swaps, their uses, pricing, and hedging, while Chapter 25 completes the swap material with a discussion of currency and commodity swaps. As we noted in the Preface, other products that bear the “swaps” moniker are discussed elsewhere in the book: volatility and variance swaps are discussed in the chapter on the Black-Scholes model, and total return swaps and credit default swaps are discussed in the chapter on credit derivative products.
Part 4 of the book (Chapters 26–30) deals with interest-rate modeling. Chapters 26
and 27 deal with the yield curve and its construction (i.e., estimation from the data). Chap- ter 28 provides a gentle introduction to term-structure modeling and its complications and discusses the different classes of term-structure models. Chapter 29 presents several well- known “factor models” of interest rates. It begins with a detailed presentation of two well- known members of the “no-arbitrage” class of term-structure models from the 1980s and
early 1990s, namely, the models of Ho and Lee (1986) and Black, Derman, and Toy (1992). Then, it develops one-factor and multi-factor models of interest rates, including, as special cases, the models of Vasicek and Cox-Ingersoll-Ross, among others. Finally, it presents the important result of Duffie and Kan (1996) on “affine” term-structure models. Build- ing on this background, Chapter 30 develops the two classes of models that have formed the backbone for much of the modeling of interest-rate risk in practice: the framework of Heath-Jarrow-Morton and that of the Libor and Swap Market models.
Part 5 of the book (Chapters 31–34) deals with credit-risk modeling and credit deriva-
tives. Chapter 31 introduces the many classes of credit derivatives and discusses their uses. Chapters 32 and 33 deal with credit risk measurement. Chapter 32 details the class of mod- els that comprise the “structural” approach to credit-risk extraction, while Chapter 33 does likewise for the “reduced-form” approach. The structural and reduced-form approaches are concerned with extracting information about the default risk of an individual entity from the market prices of traded securities issued by that entity. Chapter 34 discusses the modeling of correlated default, i.e., of modeling default risk at the portfolio level rather than at the level of the individual entity.
Part 6, the final part of the book, deals with computational methods. Chapter 35 looks
at the method of finite-differencing, and Chapter 36 describes Monte-Carlo methods. An introduction to the programming language Octave, a freeware version of Matlab that we use throughout the book for illustrative purposes, may be found in Chapter 37.