Forums > Basics > dumb Martingale question etc...

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 tw Total Posts: 4 Joined: May 2017
 Posted: 2017-06-08 18:52 Hi ChengThanks for the reply. Quick one for you. The theory gives an explicit way of constructing the risk neutralmeasure as well as stuff about existence.If you want to go about practically calculating the risk neutral measure for a process of the formdS/S = (a + f(S))dt + sigma.dWwhere f(S) is, say, -k (S-Sbar)^2k, Sbar are constants, how do you do it?Cheers!
 pj Total Posts: 3434 Joined: Jun 2004
 Posted: 2017-06-09 16:10 If your numeraire is constant (i.e. zero interest rates)dS/S=-sigma^2dt+sigma.dWfor the tradeable S.If your interest rate is a constant rthendS/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: 2863 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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