Finance 300 Financial Markets Lecture 26 © Professor J. Petry, Fall

2 Determination of Futures Prices Futures prices are based on the following theorem: Spot-futures parity theorem (aka cost of carry relationship): Describes the theoretically correct between spot and futures prices. It states that the futures price reflects the spot price of the underlying asset plus the carrying charges (cost of borrowing, storage, insurance, etc) necessary to carry the underlying asset forward to delivery. Violation of the parity relationship gives rise to arbitrage opportunities (A risk-free profit requiring no initial investment. Arbitrage often involving the simultaneous purchase and sale of essentially the same asset). Chapter VIII – Futures

3 Determination of Futures Prices Ranges for futures prices can be easily established by calculating the points at which arbitrage profits become possible. Futures prices will not remain at these levels, as market participants quickly buy up these opportunities until prices adjust them away. Example: Suppose in January 1998 the spot price of gold is $370 and the January 1999 gold futures are trading at $400. The risk free rate of interest is 5%, storage & insurance cost $1.20 per ounce. CBT gold futures trade in contracts of 100 ounces, with an initial margin requirement of $1,800. –Abitrage opportunities exist in both of the following slides. In the first we use the assumptions given above. In the second, we change the futures price from 400 to 360. Chapter VIII – Futures

4 Determination of Futures Prices Chapter VIII – Futures

5 Determination of Futures Prices Chapter VIII – Futures

6 Things To Do: VIII-7 In the previous example, at what prices to the arbitrage opportunities disappear? A) What is the expected price range for gold futures? B) What is the expected price range for 12 month gold futures when the interest rate is 15%? C) What happens to the price range when the time horizon shortens? Answer this question by looking at 12, 6, 3, and 0 month futures. Calculate the expected price range for 6 month (July ’98) gold futures when the interest rate is 15%. Calculate the expected price range for 3 month (April ’98) gold futures. And if the delivery date is tomorrow (Jan ’98). Chapter VIII – Futures

7 Financial Futures Financial Futures are futures contracts where the underlying asset itself is a financial instrument. These instruments are commonly referred to as derivates, as they derive their value from the value of an underlying asset. Futures on fixed income securities such as treasuries are referred to as interest rate futures. Short Hedge: the sale of a financial futures contract to hedge against an increase in interest rates (a decrease in the price of the asset) Long Hedge: the purchase of a financial futures contract to hedge against a decrease in interest rates (an increase in the price of the asset). Chapter VIII – Futures

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9 Miscellaneous There are a number of closely related concepts and examples in this chapter that we did not directly discuss. You are responsible for this information, and problems, with the one exception being Things To Do: VIII-12 relating to portfolio volatility. Chapter VIII – Futures

10 Chapter IX – Options

11 Options Terminology An options contract is a contract in which the writer grants the buyer the right, but not the obligation to buy from or to sell to the writer a specific asset at a specific strike or exercise price, within a specified period of time. Call Option: Grants the buyer the right to BUY the specified stock at the strike price on or before the expiry date. Put Option: Grants the buyer the right to SELL the specified stock at the strike price on or before the expiry date. Premium: The price of an option is called a premium. Strike Price: The price at which the stock is bought and sold if the option is exercised. American Option: options that can be exercised at any time prior to the expiration date. Chapter IX – Options

12 Options Terminology European Option: options that can be exercised only on the expiration date. Contract: Stock options are defined in lots of 100 shares. Index, Interest Rate and Currency Options are defined by the exchange on which the option is listed. Intrinsic Value: the profit per share if the option were exercised immediately. In-the-Money-Option: An option with a favorable exercise price in relation to the price of the underlying security. The intrinsic value is positive. Deep-in-the-Money-Option: An option with a very favorable exercise price in relation to the underlying security. Out-of-the-Money-0ption: An option with an unfavorable exercise price in relation to the price of the underlying security. Chapter IX – Options

13 Options Terminology At-the-Money-Option: An option with a strike price approximately equal to the price of the underlying security. Near-the-Money: Close, but not quite at-the-money. Examples: If IBM is trading at 50 in the spot market, how would you describe the following options (in-the-money, out-of-the- money, intrinsic value): A $45 put A $45 call A $55 call A $55 put A $50 put A $50 call Chapter IX – Options

14 Options Terminology Chapter IX – Options