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tw


Total Posts: 4
Joined: May 2017
 
Posted: 2017-06-08 18:52
Hi Cheng

Thanks for the reply.

Quick one for you. The theory gives an explicit way of constructing the risk neutral
measure as well as stuff about existence.
If you want to go about practically calculating the risk neutral measure for a process of the form

dS/S = (a + f(S))dt + sigma.dW

where f(S) is, say, -k (S-Sbar)^2

k, Sbar are constants, how do you do it?

Cheers!

pj


Total Posts: 3315
Joined: Jun 2004
 
Posted: 2017-06-09 16:10
If your numeraire is constant (i.e. zero interest rates)

dS/S=-sigma^2dt+sigma.dW
for the tradeable S.
If your interest rate is a constant r
then
dS/S=(r-sigma^2)dt+sigma.dW

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

Cheng


Total Posts: 2814
Joined: Feb 2005
 
Posted: 2017-06-11 11:28
PJ is da man!

As a sidenote, if you really want to calculate that stuff numerically you have to dig into the numerics of SDEs... I can give some more colour in case you are interested but this stuff is as charming as a visit to the proctologist.

"He's man, he's a kid / Wanna bang with you / Headbanging man" (Grave Digger, Headbanging Man)
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