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Investment / Financial Markets Old Exam MFE Forum 

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#1




Hypothetical BlackScholes Scenario
If a question gives the following information, is it possible to price a call on the stock?
(i) The stock's price follows the BlackScholes framework (ii) The stock's 1year forward price is $75 (iii) The strike price is $68 (iv) The prepaid forward annual volatility is 0.25 (v) It is a dividend paying stock. (vi) The option expires in 6 mos. (vii) The cc riskfree rate is 0.05. If it is possible, which prepaid forward price is to be used in the formula of d1: The forward price discounted back one year, or 6 mos? Thanks. 
#3




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1 year, of course.. The strike would be discounted half a year. Retracted below. Last edited by Abraham Weishaus; 03272010 at 11:41 PM.. 
#4




I don't see why Abe was saying that you should use 1 year to discount the forward price instead of 6 months.
Are you evaluating the call at t=0 or t=6 months? The evaluating date of the call would make a difference in how to solve the question. Would you be clear on that. Thanks. 
#5




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You use the prepaid forward price when pricing a call. You have the one year forward price. By definition, the prepaid forward price is the discounted value of the forward price. So discount by one year.
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#6




You're given the 1 year forward price, which is current price minus PVof dividends. You're pricing the option for 6 months. But the dividend information isn't given (is it continuous? monthly? onetime dividend paid after 6 months?).
I'm pretty sure you'd use the 6mo forward price in the BS formula, which can't be derived with the info given. If the question said "the dividend is paid next month," then you could say the 1yr forward price is the same as 6mo, and you could solve. The key info missing is when the dividend is paid. Disclaimer: I'm not extremely confident in this answer. 
#8




not that i really need to know this anymore, but i know the BS formula for a 6 month call would use the natural log of the 6 month prepaid fwd divided by the strike discounted at the risk free rate for 6 months. So i'm curious as to why you can use the 1 year prepaid fwd since it would not necessarily be equal to the 6 month prepaid fwd.
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#9




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#10




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One of those would discount dividends for a year, and one would do it for 6 months. for example, 50e^d would not equal 50e^.5d, so if the original question gave you the 1 year fwd and the 6 month fwd, you would get different answers for d1 and d2, so i must be missing something else.
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