Chapter 7, problem 4

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Chapter 7, problem 4

Postby chrissbliss » Thu Jan 20, 2011 7:16 pm

Hi Mark,

It might have been too long ago that I studied the theory of quant finance, but I got confused about the formulation of problem 7.4.
Do you mean that the spot price is normal under P ("real world measure") or under Q ("risk neutral measure")?
I thought that under a risk neutral measure the spot price is necessarily log-normal (not normal), and you cannot pass from a normal process to a log-normal one using a Girsanov-transformation since the drift is unchanged under it, right?

Maybe I think too much and should just do a simulation for an engine where the spot price is normal, ignoring whichever measure we're talking about.
Please let me know what the intention of the exercise is.
chrissbliss
 
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Re: Chapter 7, problem 4

Postby mj » Sun Jan 23, 2011 10:29 pm

in the Black-Scholes stock price increments are lognormal in any measure.

However, there are many other models.

The Bachelier model has normal increments.
mj
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