Questions / Quant research, Stochastic calculus & linear algebra
Itô on W²
Write d(W_t²) = a dt + b dW_t. What is a?
Answer it in the app It's free. You get hints, a second try if you miss, and a follow-up question.
Show the answer and worked solution
Answer: 1 drift
- Itô: df = f′ dW + ½f″ dt.
- f = x²: f′ = 2x, f″ = 2.
- Drift ½ × 2 = 1.
Interview shortcut. Itô drift is ½f″; for x², ½ × 2 = 1.
Takeaway. Itô’s lemma adds ½f″ dt because (dW)² = dt.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.