Syndicated Content Originally Posted on the Numerix Blog
By now, we all realize that financial practitioners around the globe are facing increasing challenges when it comes to computing complex risk and credit exposure calculations for both their exotic and vanilla derivative instruments. Given all we've learned about the importance of calculating counterparty risk post-2008, along with the growing need to meet ever-evolving regulatory requirements, finding more accurate and efficient ways to reign-in cumbersome counterparty exposure calculations has become more important than ever.
That's why, there's no better time than the present to explore new ways to conquer these seemingly colossal calculations. As a result, today's blog discussion will highlight some new quantitative approaches for dealing with advanced exposure and CVA for exotic and vanilla instruments, as revealed during a recent Numerix webinar conference.
"This webinar covers two important aspects of computing exposures and CVA," says Dr. Serguei Issakov, Senior Vice President of Quantitative Research and Development at Numerix. "The first part presents a general, uniform, approach to compute exposures and CVA for arbitrary deal types. This is a modern approach, which also allows aggregation of exposures across all asset classes consistently. The second part addresses special methods of fast and accurate computation of exposures and CVA for large portfolios of IR swaps, FX Forwards, and cross-currency swaps. The latter compliments the general approach and allows us to handle counterparty risk of large vanilla portions of portfolios in a more efficient way. A paper on this "superswap" approach, which is based on aggregating cashflows for linear instruments was submitted to SSRN last week. These methods are already available in Numerix products."
In the first part of the webinar, "A New Quantitative Approach: Advanced Exposure and CVA for Vanilla and Exotic Instruments," Dr. Alexandre Antonov, Senior Vice President of Quantitative Research at Numerix, discusses an algorithmic approach for Counterparty exposure calculation, automating its application to arbitrary complicated instruments. "Assuming that the portfolio is priced by the backward (American) Monte-Carlo method, our approach allows calculating the credit exposure as a pricing by-product, essentially without modifications in the usual pricing procedure," Dr. Antonov explains.
He demonstrates how this algorithmic approach is advantageous for exotic and semi-exotic instruments; and, as the webinar unfolds, we come to see how calculating exposure in parallel with pricing enables a unified, more efficient approach to be taken, when it comes to computing complex risk measures.
A New Algorithmic Exposure Approach for Exotics and Semi-Exotics
Below are some highlights to consider from this discussion; and, for a full description of this new approach, including specific examples, we recommend reading the full
technical paper [1] from the list of references.
When we look at the Exposure Calculation, the direct approach calculates all components in the backward pricing procedure and assemble them afterwards, by a forward pass. However, this requires substantial script modifications, including both backward and forward steps with a cumbersome logic of exercise indicators calculation and aggregation, Dr. Antonov explains. It can be very complicated for exotic instruments with different types of exercises, like callable instruments with automatic triggers.
Alternatively, the new approach outlined in our research —which we call the algorithmic approach— overloads continuation values operations to obtain the exposure as a byproduct of the pricing procedure. Essentially, the algorithmic exposure calculation is done in parallel with pricing. From a numerical performance perspective, it should also be noted that our exposure calculation does not significantly affect the computational effort with regard to the usual backward pricing, Dr. Antonov concludes.
A New "Thin-Out" Method for Vanillas
Below are some highlights to consider from this discussion; and, for a full description of this new approach, including specific examples, we recommend reading the full
technical paper [2] from the list of references.
In the second part of the webinar, Dr. Antonov uncovers how exposure calculation for vanilla instruments can be further optimized using a new "thin-out" method. This method reduces exposure computation time for a large portfolio of vanilla swaps to a single swap with nearly annual schedule. We come to see that the approximation quality of the "thin-out" procedure is particularly high.
The main technical tool used in this approach is a thin-out procedure for a fixed payment stream. A natural optimization for a portfolio of vanilla swaps is the aggregation of all payments into a 'superwap,' explains Dr. Antonov. Thereby, we aggregate the cashflows to represent the portfolio as a superswap.
Numerical Experiment for "Thin-Out" Method
Now, let's take a look at a numerical experiment, given the following attributes:
- Model: Hull-White 1-factor model
- Volatility = 1%, reversion = 4%, initial constant yield = 1%
- 1000 random IR swaps, with tenors out to 20Y
- Thin-out equally spaced intervals of 6M, 1Y, 2Y and 5Y
( [2] See AB (2012) for other methods of construction of thin-out dates) - Observation dates Tn are out to 20Y, at 1M intervals
- Output: Initial master Payment Stream (PS) vs. its reduced version and CVA**
In conclusion, we can see the new thin-out approach is an efficient (accurate and fast) optimization method for exposure calculation of large portfolios of IR swaps, based on a thin-out procedure of payment streams and proper handling of path-dependent streams. And, it should also be noted that this method can be easily generalized to multi-currency swaps, including CC swaps and FX-forwards.
[2] Other experiments, including exposure distribution are presented in AB (2012)
Read More
For more detailed information regarding the above, read the recently published technical papers and news release listed below:
[1] Alexandre Antonov, Serguei Issakov and Serguei Mechkov (2011),
"Algorithmic Exposure and CVA for Exotic Derivatives"
[2] Alexandre Antonov and Dominic Brecher (2012),
"Exposure & CVA for Large Portfolios of Vanilla Swaps: the Thin-out Optimization"
Numerix Introduces a New Algorithmic Method for Calculating Counterparty Exposure and its Application to Complex Risk Measures
View the webinar replay now or contact marketing@numerix.com for more information.
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