Assume the Black-Scholes framework. Three months ago, Tyler bought 100 units of an at-the-money European call option

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Assume the Black-Scholes framework. Three months ago, Tyler bought 100 units of an at-the-money European call option on a nondividend-paying stock.

He immediately delta-hedged his position with appropriate units of an otherwise identical European put option, but has not ever re-balanced his portfolio. He now decides to close out all positions.

You are given:

(i) The stock’s volatility is 36%.

(ii)

Stock price Call option price Call delta Call gamma Call theta (per year) Three Months Ago 45 ? 0.58082

Calculate Tyler’s three-month holding profit.

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