In this video blog Mohit Agarwal, Director of Financial Validation Engineering for Numerix and CMO, Jim Jockle discuss recent advancements in simulation technology, specifically counterparty credit exposure benchmarking in traditional Brute Force implementations of Monte Carlo versus American Monte Carlo.
In a new paper, Numerix benchmarks counterparty credit exposure profiles calculated with the Numerix algorithmic exposure method in the American Monte Carlo simulation against similar profiles from the foundational work of Giovanni Cesari. Conclusions show that the exposure profiles for different types of instruments computed by the Numerix algorithmic exposure method agree both qualitatively and quantitatively with the results available in the literature.
The study also compares the Numerix method to the classical Brute-Force Monte Carlo approach measuring against both accuracy and price. Mohit concludes that the algorithmic exposure simulation method agrees to high accuracy with the results obtained by the Brute-force Monte Carlo simulation, while significantly reducing the computation time.
Please note that the complete benchmarking paper discussed, "Counterparty Credit Exposure Profile Benchmarks", is protected confidential information and can only be accessed by NX users who have signed an NDA or SLA. If you are a client you can download it by simply logging into the customer support portal and clicking the title of the paper above. If you do not have access to our customer support portal please contact Numerix Support firstname.lastname@example.org for a copy of this paper.
Jim Jockle (Host): Hi welcome to Numerix video blog I'm your host Jim Jockle. With me today, Mohit Agarwal, Director of Financial Validation Engineering for Numerix. Mohit welcome.
Mohit Agarwal (Guest): Thanks Jim.
Jockle: We've been talking about many thematic issues on this video blog, especially around aggregate risk measures. And we've been focused on a lot of the challenges in terms of technology, whether it's compute, whether it's quantitative issues down to granular elements like, FVA calculation, as well as operational management. And one of the things I really want to talk to you today, is advancements that are being made in simulation technology, specifically Monte Carlo. And I know you've recently worked on a paper looking at counterparty credit exposure benchmarking in traditional brute force implementations of Monte Carlo versus American Monte Carlo which is relatively new to the market. Can you give us a little bit of a background on the differences of these two flavors of Monte Carlo?
Agarwal: Yeah definitely Jim. When we talk about counterparty credit exposure, we're talking about exposure distribution for a portfolio. And basically they're two methods of them in the market. One is the scenario approach or as we call it, the brute force way, and the other is, it's relatively new as you likely mentioned, the American Monte Carlo. It's been there for the insurance industry. It's been there for a while and now Numerix has its own implementation we call it algorithmic exposure approach. So the study was really to compare how these two approaches compare in terms of accuracy and speed.
Jockle: So what is the tradeoff? The brute force really has been the tradition and probably fast enough and accurate enough as it relates for vanilla instruments but I guess as you're bringing more exotics into the portfolio there's significant performance issues. Is it both in speed as well as accuracy? Or is it a speed issue with a brute force approach?
Agarwal: When we talk about the brute force approach it's basically two steps. So in the first step, you would generate future market scenarios. And the output would be the number of future market scenarios would be equated to the simulation paths you run your Monte Carlo for. And in the next step, you would want to price your portfolio on each of these scenarios. So basically, when you talk about vanilla versus exotics, for vanillas you have a closed form solution so it's not much of a pain. The number of calculation is not that much.
Jockle: Is that down at the pricer level, in terms of utilizing analytic pricers?
Agarwal: But when you talk about exotics, you really want to run a nested simulation that's basically Monte Carlo, over Monte Carlo, when you want to do brute force exposures for an exotics portfolio. So it becomes very computationally challenging.
Jockle: So basically if I'm understanding it correctly, you have a thousand scenarios that you are running on the pricing of the exotic, which gets overlaid against the thousands of scenarios that you're running…
Agarwal: For market scenarios.
Jockle: So now the American Monte Carlo, help me understand it, does it one set of paths that are redistributed against the model?
Agarwal: So American Monte Carlo is basically based on, we can also call it Longstaff-Schwartz Method or regression or the roll back; there are many multiple names to this method. So what it does is basically use the same Monte Carlo passage for market scenario, as well as pricing. So you technically avoid the nested simulations here, that uses regression or roll back method to find the exposures on the observation dates.
Jockle: So looking at your study, and on those two parameters of speed as well as accuracy, what were some of the key findings that you're finding in terms of performance enhancements? And is there any leakage, for lack of a better term in terms of the accuracy in those calculations?
Agarwal: So in terms of speed, the American Monte Carlo, I saw fifteen times advancement compared to brute force. And in terms of accuracy, I would say, in brute force, it's really not possible to use complex models at the second step when you're talking about a portfolio deal with both vanilla and exotics. But with Numerix algorithmic exposure you can use hybrid framework and it's possible to use the same models for pricing as well as risk. So it takes into account the correlations between the asset classes as well as with the counterparty. So it's more accurate in terms when you talk about aggregating risk exposure at the portfolio level.
Jockle: Excellent. Well Mohit thank you so much for this background and I'm looking forward to fully reading the study which will be shortly available on Numerix.com, for those who are interested in getting through for the full report. Again, we're always interested in hearing what you are saying, so please follow us along on twitter @nxanalytics or on our blog on numerix.com. Mohit thank you and we'll see you next time.