Assume the Black-Scholes framework. Four months ago, Eric bought 100 units of a one-year 45-strike European call option on a nondividend-paying stock. He immediately delta-hedged his position with shares of the stock, but has not ever re-balanced his portfolio. He now decides to close out all positions.

You are given:

(i)

(ii) The continuously compounded risk-free interest rate is 5%.

(iii) The volatility of the stock is less than 50%.

(a) Calculate the volatility of the stock.

(b) Calculate the four-month holding profit for Eric.

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Stock price Call option price Call option delta Four Months Ago $40.00 $4.45539 ? Now $50.00 ? 0.73507