hard · Quantitative Finance

In the derivation of the Black-Scholes PDE using the Feynman-Kac connection, how does the transition from a real-world measure P to a risk-neutral measure Q specifically affect the spatial operators in the PDE?

1. It eliminates the time-dependency term (partial V)/(partial t) as the process becomes a martingale.
2. It modifies only the coefficient of the first-order spatial derivative from μ S to rS.
3. It introduces a non-linear term to the PDE to account for investor risk aversion.
4. It rescales the second-order spatial derivative coefficient to account for the risk premium.

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