3. Stochastic Calculus

Itô's Formula — Quiz

Test your understanding of itô's formula with 5 practice questions.

Practice Questions

Question 1

Which of the following best describes a semimartingale, the most general class of processes to which Itô’s Formula applies?

Question 2

For a function $f(t,x)$ of class $C^{1,2}$, Itô’s Formula for the semimartingale $X_t$ includes the term $\frac{\partial f}{\partial t}(t,X_t)\,dt$. What does this term represent?

Question 3

Let $X_t$ satisfy the Itô process $dX_t = a_t\,dt + b_t\,dW_t$. Using Itô’s Formula, what is the stochastic differential of $e^{X_t}$?

Question 4

In the Itô differential $dX_t=a_t\,dt+b_t\,dW_t$, what is the correct evaluation of the quadratic variation term $(dX_t)^2$ used in Itô’s Formula?

Question 5

Let $W^1_t$ and $W^2_t$ be independent Brownian motions and define $Y_t=W^1_tW^2_t$. By the two-dimensional Itô’s Formula, which expression is correct for $dY_t$?