ecg590i_lecture03

# ecg590i_lecture03 - ECG590I Asset Pricing Lecture 3 Forward...

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ECG590I Asset Pricing. Lecture 3: Forward and Futures Prices 1 3 Forward and Futures Prices 3.1 Simple asset (no income, no costs, etc.) Basic formula F 0 = S 0 e rT where T : delivery date (time to delivery) S 0 : price of the underlying asset F 0 : forward or futures price today r : risk-free rate of interest per annum (continuous compounding) Equivalently S 0 = F 0 e ± rT : John Seater, North Carolina State University, Fall 2007

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ECG590I Asset Pricing. Lecture 3: Forward and Futures Prices 2 Market dynamics If F 0 > S 0 e rT : 1. Go long in the asset (buy the asset now) at S 0 . 2. Short forward contracts on the asset (promise to sell the asset in the future at F 0 ). = F 0 ± S 0 e rT . If F 0 < S 0 e rT : 1. Short the asset now (borrow the asset and sell it now for S 0 ). 2. Go long on forward contracts on the asset (promise to buy the asset in the future for F 0 ). = S 0 e rT ± F 0 . John Seater, North Carolina State University, Fall 2007
ECG590I Asset Pricing. Lecture 3: Forward and Futures Prices 3 S 0 is driven up (when F 0 > S 0 e rT ) or down (when F 0 < S 0 e rT ) because today arbitrageurs are trying to buy or sell. F 0 is driven down (when F 0 > S 0 e rT ) or up (when F 0 < S 0 e rT ) because arbitrageurs are o/ering to sell or buy in the future. ± Convergence S t = F t e ² r ( T ² t ) = ) S T = F T : John Seater, North Carolina State University, Fall 2007

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ECG590I Asset Pricing. Lecture 3: Forward and Futures Prices 4 3.2 3.2.1 Known income Let I 0 be the present value of the future income stream, then F 0 = ( S 0 I 0 ) e rT ) S 0 = F 0 e rT + I 0 : Intuition: ± Let T = 0 , then F is the spot price less income. ± At time T , the long forward position receives the asset minus the income stream. John Seater, North Carolina State University, Fall 2007
5 3.2.2 Known yield at the time the income is paid (e.g., a stock index). r

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## This note was uploaded on 10/05/2009 for the course ECG 590 taught by Professor Msmorril during the Fall '08 term at N.C. State.

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ecg590i_lecture03 - ECG590I Asset Pricing Lecture 3 Forward...

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