medium · Quantitative Finance
Consider f(t, x) = e^-rt x. If dX_t = r X_t dt + σ X_t dW_t, what is df?
- df = -r e^-rt X_t dt + σ e^-rt X_t dW_t
- df = (r - r) e^-rt X_t dt + σ e^-rt X_t dW_t + (1)/(2) σ^2 X_t dt
- Df = σ X_t dW_t
- df = σ e^-rt X_t dW_t
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