chapter 5 - Chapter 5 Financial Forwards and Futures...

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FINA0301 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Tao Lin Chapter 5 Financial Forwards and Futures
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Outline Financial futures and forwards On stocks and indexes How are they used? How are they priced? How are they hedged? 2
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Alternative Ways to Buy a Stock Four different payment and receipt timing combinations Outright purchase : ordinary transaction Fully leveraged purchase : investor borrows the full amount Prepaid forward contract : pay today, receive the share later Forward contract : agree on price now, pay/receive later 3
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Alternative Ways to Buy a Stock Payments, receipts, and their timing 4
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Pricing Prepaid Forwards If we can price the prepaid forward ( F P ), then we can calculate the price for a forward contract F = future value of F P Three possible methods to price prepaid forwards Pricing by analogy Pricing by discounted present value Pricing by arbitrage For now, assume that there are no dividends 5
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Pricing Prepaid Forwards (cont’d) Pricing by analogy In the absence of dividends, the timing of delivery is irrelevant Price of the prepaid forward contract is the same as current stock price Analogy (replica of prepaid forwards): the asset is bought at t = 0, delivered at t = T. 0 , 0 S F P T 6
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Pricing Prepaid Forwards (cont’d) Pricing by discounted preset value ( α : risk-adjusted discount rate) If expected time T stock price is E 0 (S T ) , then Since expected value of the stock at time T is Combining the two, 0 0 , 0 S e e S F T T P T  F P 0, T E 0 ( S T ) e  T E 0 ( S T ) S 0 e T 7
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Pricing Prepaid Forwards (cont’d) Pricing by arbitrage Arbitrage : a situation in which one can generate positive cash flow by simultaneously buying and selling related assets, with no net investment and with no risk free money!!! If at time t = 0, the prepaid forward price somehow exceeded the stock price, i.e., an arbitrageur could: buy stock and sell prepaid forward 8 F P 0, T S 0
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Pricing Prepaid Forwards (cont’d) Since, this sort of arbitrage profits are traded away quickly, and cannot persist, in equilibrium we can expect: 9 F P 0, T S 0
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Pricing Prepaid Forwards (cont’d) What if there are dividends? Is still valid? No, because the holder of the forward will not receive dividends that will be paid to the holder of the stock For discrete dividends at times t i , i = 1,…., n, the prepaid forward price: For continuous dividends with an annualized yield d, the prepaid forward price: 10 ) ( 1 , 0 0 , 0 n i t t P T i i D PV S F 0 , 0 S F P T 0 , 0 S F P T ) to 0 from paid dividends all ( 0 , 0 T t t PV S F P T T P T e S F 0 , 0 i t D
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Continuous Dividends For stock indexes containing many stocks, it is common to model the dividend as being paid continuously at a constant rate δ . Daily dividend income
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chapter 5 - Chapter 5 Financial Forwards and Futures...

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