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Long-Term Actuarial Math Old Exam MLC Forum

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Old 11-04-2001, 01:08 PM
phdmom phdmom is offline
Join Date: Nov 2001
Posts: 295

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?
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Old 11-05-2001, 02:34 AM
Kiitos Kiitos is offline
Join Date: Nov 2001
College: BYU
Favorite beer: Root
Posts: 37

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.
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Old 11-05-2001, 08:28 AM
boognish boognish is offline
Join Date: Oct 2001
Posts: 80


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

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