chapter 3.7 vs chapter 5.6

This forum is to discuss the book "the concepts and practice of mathematical finance" by Mark Joshi.

chapter 3.7 vs chapter 5.6

Postby eplask » Wed May 24, 2017 9:31 pm

In the chapter 3.7 you model the asset's real-world movement in terms of the equation:
log S_t = log S_0 + mu*t + sigma*sqrt(t)*N(0,1),
which, according to me, leads to
dS_t = S_t*[mu + (sigma^2)/2]dt + S_t*sigma*dWt.

On the other hand, in the chapter 5.6 you state that the movement is described by the geometric Brownian motion
dS_t = mu*S_t*dt + sigma*S_t*dWt.

How to reconcile the two? Do I understand correctly, that in the meantime you silently changed the definition of mu (which in 3.7 does not stand for the actual growth as there is also the "jagging condribition" 1/2 sigma^2).


Thanks in advance for clarification.
eplask
 
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