medium · Quantitative Finance

Given f(t, W_t) = t W_t, apply It^o's lemma to find df. Why is there no (1)/(2) f_xx dt term in this specific case?

1. Because the function is not dependent on t^2.
2. Because the product rule for differentials d(UV) = U dV + V dU is always sufficient for stochastic variables.
3. Because Brownian motion is a martingale, making the second-order term unnecessary.
4. Because the second partial derivative of f with respect to W_t is zero.

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