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%.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.
A) 30
B) 34
C) 69
D) 74

Question

Quizplus · Accepted Answer

Using the Black-Scholes formula, the price of the put option is found to be $5.47. The delta of the put option is -0.37, meaning that for every $1 increase in the stock price, the value of the option will decrease by $0.37. To hedge the risk, we need to short sell a certain number of shares of Alcoa's stock. This number is calculated by dividing the price of the put option by the delta, and then multiplying by 100. In this case, (5.47/-0.37) x 100 = 147.57. Rounded down to the nearest whole number, this gives us 69 shares of Alcoa's stock per 100 put options. Therefore, the answer is C) 69.

The Current Stock Price of Alcoa Is $70 and the Stock