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lima2019
Topic Author
Posts: 2
Joined: April 30th, 2020, 12:32 am

### Barrier option pricing method

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
Posts: 1749
Joined: July 14th, 2002, 3:00 am

### Re: Barrier option pricing method

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

bearish
Posts: 5532
Joined: February 3rd, 2011, 2:19 pm

### Re: Barrier option pricing method

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
Posts: 62122
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Barrier option pricing method

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
Posts: 62122
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Barrier option pricing method

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

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...

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