Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin 15-1 Understanding Futures and Options I. Analogy to Futures and Options Coin toss with two-sided potential: future Coin toss with one-sided gain: option Futures lock in prices at some specified future date. Options also lock in a future price, but do not have to be exercised. II. The Use of Futures and Options Futures and options can be used either to speculate or to reduce risk. A future or option reduces risk to the purchaser in what was previously seen as a losing state. These profits offset losses of the original investment, thereby reducing overall risk of loss.

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin 15-2 III. Forward and Futures Contracts When two parties agree to exchange a real or financial asset on a prearranged date in the future for a prespecified price, the agreement is known as a forward contract. A forward contract is a private agreement between two parties that is not a negotiable instrument. The terms can be highly customized. The forward market is an informal network consisting mostly of large corporations. A futures contract is a negotiable instrument and has standardized conditions. Standardization reduces contract flexibility but adds liquidity. Unlike forward contracts, which are not settled until termination, futures accounts must be reconciled everyday. Futures are grouped into four categories: agricultural, foreign currencies, metals and petroleum, and financial futures. Insert 15.1

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin 15-3 Relevant quotation statistics: – Opening Price – Contract Size – Settlement Price – Settlement Date – Open Interest – Trading Location – Volume of Trading Insert 15.2 IV. Valuation of Forward and Futures Contracts Apart from the nominal fee paid to execute, forward and futures contracts are nearly costless. Valuation of forward and futures contracts refers to the value of the cash or commodity flows embedded in the contract.

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin 15-4 A bank synthesizes a forward rate using the spot rate and the interest rates of both countries’ currencies. The process is: 1. Determine the appropriate forward exchange rate, F. 2. Synthesize the forward rate by borrowing dollars today, converting to the foreign currency today, and investing at the foreign interest rate. –Note that expectations do not enter the process at any point. –Futures settlement prices are determined in a manner similar to that of forward rates. –The spot price is the base figure. Added to this is the cost of carry (foregone interest, insurance, storage costs, etc.). F  S 1  r f 1  r $

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin 15-5 V. Option Contracts The owner of an option contract has the option but not the requirement to engage in the transaction. The price of the contract is the option premium. A European option can be exercised only at the end of a predetermined period. An American Option can be exercised at any time prior to expiration. A call option offers the right to buy the commodity at the exercise or strike price. A put option offers the right to sell at the exercise price. Options are traded on many exchanges, the most active being: – Chicago Board of Options Exchange (CBOE) – American Exchange (AMEX) – Pacific Coast Exchange (PSE) – Philadelphia Exchange (PHLX) Options may be as short as a few months or as long as five years. Insert 15.3

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin 15-6 VI. Futures vs. Options Revisited: Rights and Obligations Purchasers of options have rights but no obligations. Writers of options have only obligations. Buyers and sellers of futures both have the right and obligations. Insert 15.4, 15.5, & 15.6 VII. Valuation of Options Contracts Close to a dozen option pricing models have been developed for valuing options on equities, foreign currencies, commodities, and futures. The simplest model, valuation by discounting cash flows, involves taking each possible option payoff, discounting them back to the present, and weighing these present values by the probabilities of their actualization. Insert 15.7, 15.8, 15.9 & A call option’s value increases with increases in volatility. Increasing a call option’s exercise price decreases the option’s value. Increasing an option’s time to expiration increases its value.

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin 15-7 Another, and more accurate, approach to pricing options is based on arbitrage theory and involves valuation by replicating cash flows. Using other instruments, we exactly replicate the payoff patterns. The price of the option is the cost of the components. These basic techniques can be adapted to work in a variety of circumstances. The previous models assumed that price changes were made at discrete intervals. Many option pricing models are based on continuous trading arguments. These models assume a stochastic process for the prices of the underlying asset. Models whose payoffs are interest rate sensitive also assume that interest rates are stochastic. VIII. Summary Understanding the financial markets of the late twentieth century requires an awareness and knowledge of the futures and options markets. Valuing of futures and options was illustrated using discounted cash flow methodology and replication of cash flows.

Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin 15-8 IX. Appendix Option price sensitivities to changes in variables have been assigned several Greek and pseudo Greek characters. “Options As Sport” provides a clever analogy to a basketball game.