medium · Quantitative Finance stochastic
Under the Feynman-Kac theorem, how is the solution to the Black-Scholes PDE related to stochastic processes?
- It equates the physical-world drift mu directly with the risk-neutral drift r under the pricing measure.
- The PDE solution at time t can be expressed as the conditional expectation of the terminal payoff under the risk-neutral measure.
- The theorem proves that under the risk-neutral pricing measure the underlying stock price must follow an exact normal distribution.
- It shows that the Greeks of an option, such as delta and gamma, can be computed directly without differentiating the closed-form pricing formula.
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