Option pricing in continuous time makes use of Wiener processes.Which of the following is not a property of a Wiener process $W _ { t }$ ,given $W _ { 0 } = 0$ ?
A)The process has independent increments $W _ { t } - W _ { s }$
,for
$t s$
)
B)Increments are normally distributed.
C)For each $\pm$
,
$W _ { t }$
Is normally distributed with mean zero and variance
$t ^ { 2 }$
)
D)The process $\left( W _ { t } \right)$
Is a symmetric random walk around zero.

Question

Option pricing in continuous time makes use of Wiener processes.Which of the following is not a property of a Wiener process $W _ { t }$ ,given $W _ { 0 } = 0$ ?
A)The process has independent increments $W _ { t } - W _ { s }$
,for
 $t > s$
)
B)Increments are normally distributed.
C)For each $\pm$
,
 $W _ { t }$
Is normally distributed with mean zero and variance
 $t ^ { 2 }$
)
D)The process $\left( W _ { t } \right)$
Is a symmetric random walk around zero.

Quizplus · Accepted Answer

The correct variance of a Wiener process $W_t$ at time $t$ is $t$, not $t^2$. This means that for each $t$, $W_t$ is normally distributed with mean zero and variance $t$, not $t^2$.

Option Pricing in Continuous Time Makes Use of Wiener Processes WtW _ { t }Wt​

Option Pricing in Continuous Time Makes Use of Wiener Processes $W _ { t }$