medium · Quantitative Finance
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 disappear because discounting is only a risk-neutral concept.
- The first-derivative coefficient would change to μ S, but the solution would not represent a market price.
- The PDE would become elliptic rather than parabolic.
- The second-derivative coefficient would change because volatility is different under P.
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