Assume the Black-Scholes framework. Three months ago, Embryo (Ambrose’s twin brother) bought a 1-year 50-strike European cash-or-nothing call option of $1,000 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) The stock’s volatility is 30%.

(ii) The continuously compounded risk-free interest rate is 2%.

(iii)

Calculate Embryo’s three-month holding profit.

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Stock price Cash-or-nothing call option price Three months ago 50 457.5501 Now 55 606.7117