Martingale Pricing - CMG

[JohnnySinz]

Hoping someone can provide an intuitive explanation of this section of CT8; I am struggling immensely to grasp this concept.

All I understand ATM is that the probability measure Q provides a no-arb. pricing mechanism for options and P -> Q changes the stock's drift from mew to r.

What I am having trouble understanding is the use of the all the intermediary steps in the derivation of these results, specifically the Radon-Nikodym derivative. Here is a question from my university's past paper below:

Let Xt be a stochastic process defined by Xt = exp{σWt} ; Wt is brownian.
Find the following:
E[Xt*(dQ/dP)|Sigma-S] / E[dQ/dP|Sigma-S]
and E[(dQ/dP)^2|Sigma-S] / E[dQ/dP|Sigma-S]

where dQ/dP = exp{σWt− (σ^2*t)/2}

The solutions make sense algebraically although I fail to see the reasoning behind the steps :/
Any help would be greatly appreciated.

 

[Steve Hales]

Hi
The Radon-Nikodym derivative process is just another stochastic process that tells you what you need at time t to transition from one probability measure to another. As mentioned in the Course Notes, this is outside the scope of Subject CT8, but would be a great question on the Subject ST6 forum. Could I suggest moving it there? Thanks