Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a nondividend-paying stock and V (s, t) be the time-t price of a European derivative when the price of the underlying stock at that time is s. You are given:

(i) S(0) = 10 and S(2) = 12.

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

(iii) The stock’s volatility is 40%.

(iv) The following partial derivatives of V (s, t) for various s and t:

At time 0, Jason bought 100 units of the derivative. He immediately delta-hedged his position with shares of the stock, but has not ever re-balanced his portfolio. Two years later, he decided to close out all positions.

Calculate the two-year holding profit for Jason.

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S 10 12 10 12 t 0 0 2 2 V₁(s, t) -0.5861 -0.6310 -0.9804 -1.0142 V.(s, t) ? ? 0.6274 0.7825 Vss (s, t) 0.0491 0.0341 0.0946 0.0613 V(s, t) 3.2738 4.7877 ? ?