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#1
02-11-2011, 11:53 PM
 turt Member Join Date: Feb 2008 Posts: 122
ASM Black-Scholes Question

ASM (8th ed) exercise 9.16:

You are considering the purchase of a 3 month European put option on a stock with an announced dividend payment of 1.50 in 2 months
K = 50
r = .10, comp cont
volatility of 3-month prepaid fwd on stock = 0.3
stock follows B-S framework
d_2 = -0.1086
Determine the stock price

The solution is set up with -0.1086=(ln(F^p/50) + (0.1-0.5*0.3^2)(.25)) / ((0.3)(sqrt(.25))

where F^p is the prepaid forward price of the stock. After solving for F^p, you can easily find S.

I set it up with 50e^(-.10/4) instead of plain 50. I thought since we were using the prepaid forward in the numerator, we needed the same in the denominator. What am I missing?

Gracias.
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#2
02-11-2011, 11:58 PM
 herrMrtn Member SOA Join Date: Jan 2011 Location: Hong Kong College: University of British Columbia '10 Posts: 215

If you used 50e^(-.10/4), then you need to drop the 0.1*0.25 in the numerator. Remember that when you're using prepaid forward prices, you need to drop the div and risk-free rate from the numerator of the equation for d_1 and d_2; the prepaid forward prices already account for those.

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#3
02-12-2011, 12:27 AM
 turt Member Join Date: Feb 2008 Posts: 122

Of course! So simple, I just did it correctly on a different problem without even thinking.
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