No Slide TitleFourth Edition
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______ value -
2
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Option
value
X
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Factor Effect on value
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Borrow $_____ (8% Rate)
Net outlay $53.70
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Alternative Portfolio - _____ share of stock and ____ calls written (X = 125)
Portfolio is perfectly hedged
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d2 = d1 - (s T1/2)
So = Current stock price
N(d) = probability that a random draw from a normal dist. will be less than d.
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e = 2.71828, the base of the nat. log.
r = Risk-free interest rate (annualized continuously compounded with the same maturity as the option.
T = time to maturity of the option in years.
ln = Natural log function
s = Standard deviation of annualized cont. compounded rate of return on the stock
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s = .50 d = 0
= ____
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Call Option Value
Co = Soe-dTN(d1) - Xe-rTN(d2)
Co = 100 X .6664 - 95 e- .10 X .25 X .5714
Co = 13.70
Implied Volatility
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Using the sample data
P = $95e(-.10X.25)(1-.5714) - $100 (1-.6664)
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P = C + PV (X) - So
= C + Xe-rT - So
P = ____
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Call = N (d1)
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Buying Puts