The current stock price of Alcoa is $115, and the stock does not pay dividends. The...

The current stock price of Alcoa is $115, and the stock does not pay dividends. The instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of Alcoa's stock is 35%. You want to purchase a put option on this stock with an exercise price of $120 and an expiration date 30 days from now. According to the Black-Scholes OPM, you should hold __________ shares of stock per 100 put options to hedge your risk.

Expert Solution

Input Data
Stock Price now (P)		115
Exercise Price of Option (EX)		120
Number of periods to Exercise in years (t)		0.082191781
Compounded Risk-Free Interest Rate (rf)		6.00%
Standard Deviation (annualized s)		35.00%


Output Data
Present Value of Exercise Price (PV(EX))		119.4097
s*t^.5		0.1003
d1		-0.3248
d2		-0.4252
Delta N(d1) Normal Cumulative Density Function		0.3727
Bank Loan N(d2)*PV(EX)		40.0448

Shares to hold= [Number of option-(N(d1)X100)]

=100-0.3727*100 = 62.73

Therore shares to hold =63

jeff jeffy answered 2 years ago

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