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Let $\tau =T-t$. Conditional on ${\mathcal{F}}_t$ under the risk-neutral measure,Using the moment-generating function of a normal distribution in the risk-neutral expectation gives the Power payoff in the Black-Scholes model valueIn particular,The delta hedge holdsunits of the risky asset.

Risk-neutral valuation givesSince $W_T^Q\sim N(0,T)$,Hence the Power payoff in the Black-Scholes model has price