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April 8th, 2012, 12:21 PM   #1
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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
manchester20 is offline  
 
August 23rd, 2012, 03:47 AM   #2
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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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