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Barrier option pricing method

Posted: May 20th, 2020, 9:54 am
by lima2019
Dear all, 

I would like to ask a question about how to calculate delta of UP-and-Out barrier call in close-form formula. Also, I understand there is close-form solution for very std barrier option. I wonder why some papers still use finite difference method or monte carlo simulation to either price the option or calculate delta.

Many thanks

Re: Barrier option pricing method

Posted: May 20th, 2020, 11:30 am
by DavidJN
When the tool in your toolbox is a hammer, every problem looks like a nail.

Re: Barrier option pricing method

Posted: May 20th, 2020, 4:37 pm
by bearish
To expand slightly, the closed form solutions require very strict assumptions on the underlying price process, whereas MC and grid based methods can handle more general processes (e.g. time and/or level dependent volatility).

Re: Barrier option pricing method

Posted: May 20th, 2020, 7:41 pm
by Cuchulainn
My book on C++ 2nd edition does PDE/FDM for barriers. I would not be a fan of MC nor lattices for this, and Greeks is messy.

https://www.datasim.nl/blogs/13/summary


https://www.datasim.nl/application/file ... hesis_.pdf

Re: Barrier option pricing method

Posted: May 20th, 2020, 7:47 pm
by Cuchulainn
 I wonder why some papers still use finite difference method or monte carlo simulation to either price the option or calculate delta.

I wonder why people such as yourself think this in the first place. Nothing personal. It's my duty to ask.


https://forum.wilmott.com/viewtopic.php?f=19&t=23637

Proposed by Cuchulainn. His suggestion also gives a few clues about why closed-form solutions may not be as useful as you might think:"What is the added value of closed [-form] solutions if 1) they are based on an ANSATZ and 2) they are incredibly difficult to solve numerically? Example: The Heston 1993 paper 1) he assumes solution in a special form and 2) brittle complex integral"P

I hate ANSATZs (aka Guesstimates), it's like separation  of variables in PDE   We give it a German name to make it sound nice.

It's almost as bad as saying that PDEs have far-field boundary conditions: they don't