medium · Quantitative Finance stochastic
The Feynman-Kac theorem relates the Black-Scholes PDE to the expectation under the risk-neutral measure.
If we were to use the physical measure P, what would happen to the PDE?
- The term -rV would vanish entirely, since discounting future cash flows is purely a risk-neutral device.
- The first-derivative coefficient would change to μ S, but the solution would not represent a market price.
- The PDE stays parabolic; that classification depends on the highest-order derivative terms, not drift.
- The second-derivative coefficient stays unchanged, since Girsanov's theorem says volatility is measure-invariant.
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