I am working on a project related to Nonlinear BS partial differential equation, with terms for transaction costs and/or discrete hedging. I have two questions:

  1. Is there any exact solution to the Nonlinear BS equation?

  2. I have read a paper which numerically solved a Nonlinear BS and compared results with Linear BS. Nonlinear BS is supposed to be giving different option price than Linear one. Why should we compare them ? the paper

Lastly, as I am working on a project , it will be extremely helpful if you can provide some references that backs your statements.


1 Answer 1


In general you have don't have an exact solution for the non linear equation - so you have to use numerical methods. Have you seen this Non linear option pricing book. It covers the topics that you mentioned.

People generally do compare the prices produced by non traditional models to the traditional ones - the purpose could be to benchmark the model output, understand/locate the regions where the prices differ, or to demonstrate the superiority of the new model etc.

  • $\begingroup$ I understood what you are saying. Still I needed a more accurate answer for the second question. Nonetheless,Thank you. $\endgroup$
    – user1157
    Dec 20, 2019 at 23:44
  • $\begingroup$ thanks! by the looks of it, the author is trying to demonstrate that the difference to Black Scholes is economically significant, and varies by maturity etc., so the non-linear models are informative/value adding in a sense $\endgroup$ Dec 21, 2019 at 0:02

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