Jul 9, 2013

Derivatives Funding Dynamics and SABR Spreads its Wings - A Quantitative Update

Watch the Video: Derivatives Funding Dynamics and SABR Spreads its Wings - A Quantitative Update

In this video blog CMO, Jim Jockle and Alexander Antonov, Senior VP of Quantitative Research discuss the latest research & insights from Numerix's global Quantitative Research Group. Alexander unveils a new universal framework for Funding Value Adjustment (FVA) calculation, discussing the practical implementation and market use-case.

Download a copy of the full paper: Funding Value Adjustment for General Instruments: Theory and Practice.

Alexander then shifts focus to Numerix's latest achievement around the Stochastic Alpha Beta Rho (SABR) model – the industry standard for Interest Rate Derivatives – and shares insights from Numerix's new research paper SABR Spreads its Wings, published in the August issue of Risk Magazine.

Weigh in and continue the conversation on Twitter @nxanalytics, LinkedIn, or in the comments section. 

Jim Jockle (Host): Hi welcome to Numerix Video Blog, I'm your host Jim Jockle. And welcome to a Summer Friday Edition of the Numerix Video Blog. How's it going Alexander?

Alexander Antonov (Guest): I'm fine. Thank you Jim.  

Jockle: Well today I really want to do what I'd like to call a quantitative preview. I think a lot of exciting work has been coming out of your group, and just to give a heads up on what's coming out in the next few weeks within CrossAsset as well as some new research that you have produced. So the first thing I want to talk about is really a new universal framework for FVA – funding valuation adjustments that is being introduced within the Numerix stack. And what is being implemented really is an expansion upon Vladimir Piterbarg's framework for the valuation and the presence of real collateral.

Perhaps you could just take a few minutes and walk us through the implementation in how this really scales beyond into a practical use framework.  

Antonov: Sure. I have generalized the framework of Vladimir Piterbarg to general instruments. So basically whatever model, whatever barrier instruments can be put in this framework is calculated. I also came up with a universal formula for that, we have a single formula to be implemented which produces in all the simple and exactly solvable cases an exact result.

This framework was put into the CrossAsset, again in a universal way. We're using our technology of algorithmic exposure calculation for each of our instruments. This doesn't change, there's absolutely no difference with CVA, we reused the exposures, and then we aggregate them using scripting language in the FVA; which is good that you can take whatever instrument and calculate automatic exposures without any changes. 

And then we plug the exposure of the whole portfolio set of instruments, inside the FVA script – a new entity in the CrossAsset, which can give you the results in all the universality of your collateral, of the funding rates, of the collateral rates and all these fine details that are very important in banks. So using the script, we can cover almost all the CSA agreement

Jockle: And in this implementation you're also addressing the computational overhead as well by reutilizing the path. So you're looking at the one element of reuse for better granularity. Is that accurate?

Antonov: That's right. We reuse the paths coming from the models of the instruments into the FVA presentation. And the theoretical background underlying this implementation was recently produced in terms of the article to the SSRN, which was written with Marco Bianchetti from Intesa and also Ion Mihai, our colleague from Paris quantitative support. And we have produced of course theoretical results, underlying the FVA.

And also some practical experiments, which to our knowledge was never done before. If we consider FVA of even a simple object, the numerical procedure is quite complicated. So it passes through all the difficulties and at the end, we have done numerical experiments of Bermudan option and the swap in that combination, and then compared our FVA result and we found the approximation was excellent in this case. 

Jockle: And so I want to step back and really just thinking about that, and for those who are interested in the funding valuation for a general financial instruments, the theory and the practice document – it is available on SSRN, as of May 28th of this year and that was coauthored with Alexander as well as Marco Bianchetti and Ion Mihai, but also I want to turn to something that continues to be of note.

Going back to Wilmott last year, with Michael Spector and some work by yourself, and now an upcoming paper in Risk Magazine titled, SABR Spreads it's Wings, where is the world of SABR at this point in time because it's been so much back into the press, and maybe a little bit of a primer of where we are with the SABR Model. 

Antonov: Sure. The SABR Model is used by practitioners to interpolate the volatility surface, in the interest rate business. So it'll have a swaption with different strikes corresponding to the same maturity and the length. And then they produce the so called implied volatility smile. So this volatility smile is quoted by only certain points of the smile, certain strikes, and of course the practitioner wants to extrapolate / interpolate, in other words to calculate for other strikes for example far wings of the smile. Also, one of the related problems calculated the CMS products, which in done using this extrapolation and interpolation, so the nice precision of this formula for large strikes, is a key here. 

In early 2000, Hagan and co-authors had written the nice and very famous approximation formula for the implied volatility, which appears to be very good, not far from at-the-money, strikes and for relatively short maturities. For longer maturities, which are always present in the interest rate business up to thirty years, and quite far strikes, which are also important as we said about the CMS rates, this one can give very strange results leading to for example negative probabilities, probabilities tends to, which we know it doesn't exist in the nature – fortunately or unfortunately. 

So in our paper we have written, we have two results. The first one is for zero correlation, that's one of the parameters for the SABR Model have produced an exact result. Which can be translated into one dimensional numerical integration. I just want to mention that the Hagan formula is just using the normal functions, it's not in the numerical observation. However this is slightly, probably ten times slower.

However the accuracy is excellent, as far as its exact. And the second result for all the other correlations, the result is a very good approximation. Which behaves very well even on the wings, on the edges of this distribution. So our paper will be called in the Risk Magazine, SABR Spreads it's Wings in product manner of the Risk Magazine. It will be issued in August this year, and we'll have written it with Michael Konikov and Michael Spector, our Numerix colleagues.         

Jockle: Excellent. Well Alexander, thank you so much for the update. Looking forward again - Risk Magazine in August so be sure to get a copy. And any questions on that we can definitely make sure we can connect you with Alexander and the team to address that. So again follow us along on twitter @nxanalytics or on LinkedIn, on our company page to stay abreast to all that's coming out to the market, as well our Thought Leadership on issues facing todays OTC markets. Alexander thank you so much for joining us, and we'll talk next time. 

Antonov: Thank you. It was a pleasure and privilege for me also.       

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