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I am new to the quantitative finance side of things( came from mathematical physics). I'm currently investigating numerical techniques for solving BS, which made realise when are numerical techniques actually required in the first place(i.e. no analytic closed form solution). Any help on this matter would be much appreciated.

Regards, Eddie

user67120
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    You would typically use numerical techniques - for example - if the option price is dependent on the path (such as knock-out or knock-in options, range accruals, american options, etc). Then, the grid of values along the time-domain is important for the computation, not just the terminal value (which in the simple BS model for vanilla options can be computed analytically). – Jan Stuller Apr 20 '23 at 15:03

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As previously stated, analytical solutions in option pricing are the exception. So indeed, as Jan Stuller points out, numerical techniques are the tool to solve many problems.

To answer your question, within the context of the Black Scholes Merton model, there is one use of numerical techniques I can come up with: calculating the implied volatility when all the other parameters and price are known. Of course, this has been studied, see this question.

Hans-Peter Schrei
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Bob Jansen
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