My Math Forum Finding the general solution to the Black Scholes PDE

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 April 8th, 2012, 11:21 AM #1 Newbie   Joined: Apr 2012 Posts: 1 Thanks: 0 Finding the general solution to the Black Scholes PDE Hello, I have the PDE -?v/?? + 1/2(?^2)(?^2)?^2v/??^2 + (1/T +(D-r)?)?v/??=0 and firstly I need to seek a solution of the form v=?1(?)? + ?0(?) and then determine the general solution for ?1(?) and ?0(?). I am given that ?=I/TS - X/S and ?=T-t. Could anybody help me with this? Thanks
 August 23rd, 2012, 02:47 AM #2 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 Re: Finding the general solution to the Black Scholes PDE Hey manchester29. There is a book by Wilmott, Howison, and DeWynne called "The Mathematicas of Financial Derivatives" that goes over the proof to transform the BS to a PDE and then uses what is called the "Heat equation" to get the final log-normal PDF. http://www.amazon.com/The-Mathematics-F ... 0521497892 It goes into a lot of detail for these kinds of problems and if you are going to be doing this for a while you should get something like it.

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