Barrier option pricing method

lima2019 · May 20th, 2020, 9:54 am

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

DavidJN · May 20th, 2020, 11:30 am

When the tool in your toolbox is a hammer, every problem looks like a nail.

bearish · May 20th, 2020, 4:37 pm

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).

Cuchulainn · May 20th, 2020, 7:41 pm

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

Cuchulainn · May 20th, 2020, 7:47 pm

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

Barrier option pricing method

Barrier option pricing method

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