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Difficulty: Hard
Category: Stochastic Calculus
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Topics: Black-Scholes, PDE, Stochastic Calculus, Derivatives Pricing
Consider a European option with price $V(S, t)$, where $S$ is the underlying asset price and $t$ is time. The option's price evolves according to the Black-Scholes framework. Assume the underlying asset follows a geometric Brownian motion with volatility $\sigma$ and the risk-free interest rate is $r$.
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