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April 8th, 2012, 11:21 AM   #1
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Finding the general solution to the Black Scholes PDE

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



Could anybody help me with this?

manchester20 is offline  
August 23rd, 2012, 02:47 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. ... 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.
chiro is offline  

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