Assume the Black-Scholes setting for an arbitrage-free financial market, i.e.

| August 14, 2017

Assume the Black-Scholes setting for an arbitrage-free financial market, i.e.
dS(t) = rS(t)dt + σS(t)dW˜ (t) and S(0) = S0.
Consider a European security with payoff ST2.
A)Find the arbitrage-free price of this security V0 at time 0. B)Write down the arbitrage-free price of this security at time t, as a function of t and S. C)Show that the function you have had in part (b) satisfies the Black-Scholes PDE and its terminal condition.

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