Question

The current stock price of Alcoa is $90, 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 30%. You want to purchase a put option on this stock with an exercise price of $95 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.

	31
	35
	70
	75

Answer 1

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Answer:

d1 = (ln(S/K) + (r + (s^2)/2)t)/(s*root(t))

d2 = d1 - s*root(t))

where S= current stock price

K = option strike price

t = time to maturity

s = volatility

r = risk free rate

c = call premium

d1 = (ln(90/95) + (.06 + (.30^2)/2) * .083)/(.30*root(.0833))

= -.523787

d2 = -.523787- .30*root(.0833)

= - .61037

N(d1) = can be found using the z -table and it is the call option's delta value.

N(d1) = Norm.DIST(-523787, 0,1, True)

= 0.300

Shares to hold = 100-0.300*100

= 100-30

= 70