medium · Quantitative Finance
The Feynman-Kac formula connects the expectation V(S, t) = E^Q[e^-r(T-t) Psi(S_T)] to the PDE V_t + mathcalAV - rV = 0.
For a standard stock process, what does the infinitesimal generator mathcalA represent in financial terms?
- The cost of carry that must be paid to continuously maintain a delta-neutral hedge in the underlying asset.
- The expected instantaneous change in the option price due to movements in the underlying under the risk-neutral measure.
- The sensitivity of the option's price to shifts and twists in the entire implied volatility surface, commonly denoted Vega.
- The total risk premium an investor demands as compensation for bearing the risk of holding the derivative until its maturity date.
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