# ftT - t = stock price at t I t = value at time t of...

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Stat/Actsc 446/846: Mathematical Models in Finance – Fall 2010 Example on forward contracts with dividends Example: A stock costs \$100 at time 0 and is expected to pay a quarterly dividend of \$1.25 over the next year. The interest rate is 10% (continuously compounded). (a) What is the forward price F = F (0 ,T ) for a contract struck at time 0 and with maturity in T = 1 year? (b) If the stock price is \$105 after 6 months, then what is the forward price for a forward contract struck at time t = 0 . 5 with an expiration time at T = 1 year? Solution: (a) Using the formula seen in class, we have F ( t,T ) = ( S t - I t ) e r ( T - t ) , where S
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Unformatted text preview: t = stock price at t I t = value at time t of cashﬂows to be received over the life of the contract . In this case we want F = F (0 , 1) = 100 e . 1 × 1-4 X i =1 1 . 25 e . 1(1-t i ) where t i = 0 . 25 i , so F = 105 . 33. (b) We want F ( t,T ) with t = 0 . 5, T = 1. We have that S t = 105, and I t = 2 X i =1 1 . 25 e-. 1 × . 25 i = 1 . 25 e-. 1 × . 25 + 1 . 25 e-. 25 × . 5 = 2 . 408 because a dividend of \$1.25 will be received at time 0.75 and at time 1. Therefore F (0 . 5 , 1) = (105-2 . 408) × e . 1 × . 5 = 107 . 85 . 1...
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