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Papero
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Joined: July 14th, 2002, 3:00 am

### Monte Carlo simulation of SABR model

Dear members,
I am looking for any paper comparing the SABR approximated formulas against a MC simulation.
I found a couple of papers by OOsterlee et al. but, in my opinion, they are too complex to start with, I am looking something basic.
Thank you in advance for any suggestion!

Alan
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### Re: Monte Carlo simulation of SABR model

Presumably, you will use the MC as a proxy for 'exact'. If so, I can point you to a source for actual exact -- at least for the lognormal SABR model. See Ch. 8 of my 'Option Valuation under Stochastic Volatility II' book.

While my derivations are complicated, you can just trust me that the tables are correct -- at least until you've found a MC source that you like and can code yourself.  As a rule of thumb, everything in finance should be calculated 3 different ways anyway!

Cuchulainn
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### Re: Monte Carlo simulation of SABR model

Some alternaties

1. Machine Learning
https://www.datasim.nl/application/file ... 423101.pdf

2. PDE approach using ADI, for example. I think Joerg Kienitz is active here.

3. If SABR is like Heston, then standard FD and MC will have a lot of bias (i guess). You could try a basic Euler to see if it is good ..

Joerg and I did a bunch of FDM for Heston in our C# MC book and QE2 was best. Here's the same idea for SABR

https://papers.ssrn.com/sol3/papers.cfm ... id=2575539
Last edited by Cuchulainn on September 20th, 2020, 7:17 pm, edited 1 time in total.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

Alan
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Joined: December 19th, 2001, 4:01 am
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### Re: Monte Carlo simulation of SABR model

Also, this old thread, unfortunately somewhat corrupted, has a nice tricky case for testing putative SABR MC's or other approaches.

Cuchulainn
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Joined: July 16th, 2004, 7:38 am
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### Re: Monte Carlo simulation of SABR model

Also, this old thread, unfortunately somewhat corrupted, has a nice tricky case for testing putative SABR MC's or other approaches.
'somewhat'.

"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

Alan
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### Re: Monte Carlo simulation of SABR model

I didn't want to completely discourage the OP from clicking on it.

Cuchulainn
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### Re: Monte Carlo simulation of SABR model

I didn't want to completely discourage the OP from clicking on it.
I've seen worse, e,g. my $e^5$ and the horrendous Heston benchmark.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler

http://www.datasimfinancial.com
http://www.datasim.nl

JohnLeM
Posts: 515
Joined: September 16th, 2008, 7:15 pm

### Re: Monte Carlo simulation of SABR model

Dear members,
I am looking for any paper comparing the SABR approximated formulas against a MC simulation.
I found a couple of papers by OOsterlee et al. but, in my opinion, they are too complex to start with, I am looking something basic.
Thank you in advance for any suggestion!
In a second step, once the method acquired (come on, it is a quite straightforward method), toy trying to code it to best learn !
If you look to a table with strikes and values to benchmark your own implementation (taken from Exact Analytical Solution for the Normal SABR Model)
I am quite sure that there exists open source (R, python, C++) doing right that. If not I can provide some R code, Quantlib C++ do this also very well I guess.