Option pricing models are based on Ito processes. Which of the following statements best describes Ito processes? Ito processes $Y _ { t }$ are
A) A special case of Wiener processes $W _ { t }$ .
B) Are functions of Wiener processes: in SDE form, $d Y ( t ) = a d t + b d W ( t )$ .
C) Are functions of Wiener processes: in SDE form, $d Y ( t ) = a d t + b d W ( t )$ , with the restriction that $\alpha$ and $b$ have to be constants.
D) Are functions of Wiener processes: in SDE form, $d Y ( t ) = a d t + b d W ( t )$ , with the restriction that $\alpha$ and $b$ have to be constants or functions of time $t$ alone.

Question

Quizplus · Accepted Answer

Ito processes are indeed functions of Wiener processes, described by stochastic differential equations (SDEs) of the form $dY(t) = a dt + b dW(t)$, where $a$ and $b$ can be functions of both the process $Y$ and time $t$, not necessarily constants or functions of time alone.

Option Pricing Models Are Based on Ito Processes YtY _ { t }Yt​

Option Pricing Models Are Based on Ito Processes $Y _ { t }$