The current stock price of Alcoa is $110, and the stock does not pay dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard deviation of Alcoco's stock is 30%. You want to purchase a put option on this stock with an exercise price of $115 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.

Explanation:

d_1 = (ln(S/K) + (r + (s^2)/2)t)/(s√(t))

d_2 = d_1 - s√(t))

where S= current stock price

K = option strike price

t = time to maturity

s = volatility

r = risk free rate

c = call premium

d_1 = (ln(70/75) + (0.06 + (0.40^2)/2)× 0.083)/0.40√(.0833)

= -0.49646

d_2 = -0.49646 - .40√(.0833)

= -0.61193

N(d_1) = can be found using the z -table and it is the call option's delta value.

N(d_1) = N(-0.49646) = 0.31

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