N
Niall1234
Member
I'm having trouble understanding the solution to part (ii).
It's only worth 2 marks so should be straight forward.
I have to find E[St] = E[exp^B(5)], where B(5) is standard brownian motion.
From the notes, the expected value of a security price at time t using Geometric brownian motion is :
E[St] = exp((Zo + mu*t) + 0.5 *sigma^2*t)
As B(5) - N(0, 5), I would expect that, E[S(5)] = exp((0+0*5)+0.5*5*5)= exp(12.5),
Where, mu=0, sigma^2=5, t=5, Zo=0
However in the solutions they end up with a much different answer, and E[S(5)] = exp(0.5*5*1^2), so I'm not sure where the 1^2 is coming from.
Any help would be greatly appreciated.
It's only worth 2 marks so should be straight forward.
I have to find E[St] = E[exp^B(5)], where B(5) is standard brownian motion.
From the notes, the expected value of a security price at time t using Geometric brownian motion is :
E[St] = exp((Zo + mu*t) + 0.5 *sigma^2*t)
As B(5) - N(0, 5), I would expect that, E[S(5)] = exp((0+0*5)+0.5*5*5)= exp(12.5),
Where, mu=0, sigma^2=5, t=5, Zo=0
However in the solutions they end up with a much different answer, and E[S(5)] = exp(0.5*5*1^2), so I'm not sure where the 1^2 is coming from.
Any help would be greatly appreciated.