Question

1. The current stock price of Alcoa is $70, 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 40%. You want to purchase a put option on this stock with an exercise price of $75 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.
   

   		30
   		34
   		69
   		74

Answer 1

Solution) The correct answer is C, i.e., 69

The number of shares to be held against per 100 put options can be calculated using the Delta (Hedge ratio)

Delta = N(d1)

d1 = [ln(70/(75*e^(-6%*30/365)) + (0 + 40%^2/2)*30/365]/40%*sqrt(30/365)

= [ln(70/74.63105) + 0.08*30/365]/0.114676

= [-0.06406 + 0.006575]/0.114676

= [-0.05749]/0.114676

= -0.5013

Delta can be found in Excel as = NORMSDIST(-0.5013) = 0.31

Hence for 100 put options number of stock to buy = (1 -0.31)*100 = 69

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