# The forward price may be different for contracts of

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The forward price may be different for contracts of different maturities. 11

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The forward price ( F τ |t ): is the sum of two components: Expected value of the spot price at time τ , E(S τ )=S 0 . A compensation for the party taking the short position for the loss of investment income occasioned by holding the asset ( R) . Suppose the contract is to mature in one year. Then: F 1|0 = S 0 (1+r) 12
Example: Consider a stock that pays no dividend and is worth £10 today ( S 0 =£10 ). Suppose the current annual interest rate is r=5% (you can borrow or lend money at 5%). What should the 1-year forward price of the stock ( F 1|0 ) be? F 1|0 = S 0 (1+r) = 10 (1.05) = 10.5 13

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Why? If F 1|0 > S 0 (1+r) you could: borrow S 0 today for 1 year, buy the asset, engage in a forward contract to sell it in 1 year for F 1|0 . and make a profit of F 1|0 - S 0 (1+r) > 0 14
Why? If F 1|0 < S 0 (1+r) an investor owning the asset could: Sell the asset today for S 0 , Invest the proceeds to get S 0 (1+r) in 1 year, enter in a forward contract to buy the asset back in 1 year. make a profit of S 0 (1+r) - F 1|0 > 0 15

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More generally ( τ > 1) : If the spot price of gold is S 0 and the forward price for a contract deliverable in τ >1 years is F τ |0 , then F τ |0 = S 0 (1+ r ) τ where r is the 1-year (domestic currency) risk-free rate of interest. 16
Forward contracts on foreign exchange: A popular example used to hedge foreign currency risk. 17

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On July 20, 2007 the treasurer of a corporation enters into a long forward contract to buy £1 million in six months at an exchange rate of 2.0489 This obligates the corporation to pay \$2,048,900 for £1 million on January 20, 2008 What are the possible outcomes? 18
19 Bid Offer Spot 2.0558 2.0562 1-month forward 2.0547 2.0552 3-month forward 2.0526 2.0531 6-month forward 2.0483 2.0489

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20 Profit Price of Underlying at Maturity, S T K τ S T - K τ
21 Profit Price of Underlying at Maturity, S T K K τ - S T

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Agreement to buy or sell an asset for a certain price at a certain time. Similar to forward contract. Whereas a forward contract is traded in OTC markets, a futures contract is traded on an exchange. 22
Agreement to: Buy 100 oz. of gold @ US\$900/oz. in December (NYMEX) Sell £62,500 @ 2.0500 US\$/£ in March (CME) Sell 1,000 bbl. of oil @ US\$120/bbl. in April (NYMEX) 23

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A call option is an option to buy a certain asset by a certain date for a certain price (the strike price).
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• Spring '12
• D.S.G.Pollock
• John C. Hull

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