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An option that can be exercised only at expiration.

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How do I prove that a certain price is price of European option in Black-Scholes framework

Yes it is actually just substituting it into the Black Scholes PDE. If the PDE is satisfied, $V(t,S(t)),t\ge 0$ is a martingale and hence $V(t,S(t)) = E_t (V(T,S(T))$ so that $V(t,S(t))$ is the expect …
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