Course 3 May 2001 #8

[phdmom]

This is how I would work this problem...

P(t)=100e^(.01 + .02Y(t)) where Y(t) is standard Brownian motion. Y(1) is N(0,1), so the simulated value .1587 gives Y(1)=-1 and P(1) = 99. Y(2) is N(0,2), so the simulated value .9332 gives Y(2)=1.5*sqrt(2) and P(2)=104, for a difference of 5. Wrong answer.

Can anyone tell me what's wrong with the above reasoning?

[Kiitos]

The problem in your logic comes when you get the second simulated value. Y(2) is not N(0,2), but N(0,1). The reason for this comes that we assume that after the first simulated number, we start over again. Hope that helps.

[boognish]

PhdMom,

I think the key is when they state in the problem that "simulation projects the stock price in steps of time 1"