Nneetquant
Get started

Variance of a stochastic integral

MediumProbabilityStochastic Processes~4m

Let I=∫03t dWtI = \int_0^3 t\,\mathrm{d}W_t, where WtW_t is standard Brownian motion. What is Var⁡(I)\operatorname{Var}(I)?

Show hints (2)+
  1. E[I]=0E[I]=0 (martingale), so Var⁡(I)=E[I2]\operatorname{Var}(I)=E[I^2].
  2. Itô isometry: E[(∫03t dWt)2]=∫03t2 dtE[(\int_0^3 t\,\mathrm{d}W_t)^2]=\int_0^3 t^2\,\mathrm{d}t.

Answer

Reveal answer →

9 (± 0.001)

Create a free account to see the full worked solution and track your progress.

Create a free account

Interview format: Market Maker, Hedge Fund Quant

Related questions