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Papero
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Monte Carlo simulation of SABR model

September 20th, 2020, 11:38 am

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!
 
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Alan
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Re: Monte Carlo simulation of SABR model

September 20th, 2020, 6:43 pm

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!  :D

 
 
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Re: Monte Carlo simulation of SABR model

September 20th, 2020, 7:07 pm

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.
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Alan
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Re: Monte Carlo simulation of SABR model

September 20th, 2020, 7:12 pm

Also, this old thread, unfortunately somewhat corrupted, has a nice tricky case for testing putative SABR MC's or other approaches.
 
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Re: Monte Carlo simulation of SABR model

September 20th, 2020, 7:18 pm

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

Image
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Alan
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Re: Monte Carlo simulation of SABR model

September 20th, 2020, 7:37 pm

I didn't want to completely discourage the OP from clicking on it. 
 
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Re: Monte Carlo simulation of SABR model

September 20th, 2020, 7:49 pm

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.
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JohnLeM
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Re: Monte Carlo simulation of SABR model

September 20th, 2020, 10:40 pm

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.