Questions / Quant research, Stochastic calculus & linear algebra
Itô isometry
What is Var(∫₀³ s dW_s)?
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Answer: 9 variance units
- Isometry: Var(∫f dW) = ∫f² ds.
- ∫₀³ s² ds = 27/3 = 9.
Interview shortcut. Isometry: Var = ∫s² ds = T³/3 = 27/3.
Takeaway. Itô isometry turns stochastic variance into an ordinary integral.
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