Banks look to cut corners on CVA computation

Calculating credit value adjustment correctly for exotic instruments can require the simulation of scenarios within scenarios – and today’s computers may not be up to it. As a result, banks are looking for short cuts, and they may be able to learn from the insurance industry. By Clive Davidson

tom-wilson
Thomas Wilson

Banks look to cut corners on CVA computation

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Banks look to cut corners on CVA computation

Todya's computers are being pushed to their limits by modern pricing and risk management practices, which often rely on stochastic analysis in the form of Monte Carlo simulation. These processes require the value of trades and portfolios to be calculated for a range of subtly differing scenarios. That generally takes massed computing power in the form of networked grids of processors – but it is not always enough.

Certain portfolios or products can require additional stochastic analysis if their value is to be correctly simulated – so-called stochastic-on-stochastic or nested stochastic analysis. This can magnify the computational problem by several orders of magnitude – 10,000 so-called outer scenarios might each require 10,000 inner scenarios – making it impossible to solve the problem in a usable time frame.

Calculating the credit value adjustment (CVA) for exotic instruments under Basel III is just such a problem. Exotic instruments such as American-style options or Bermudan swaptions that can be called at various dates prior to maturity need to be priced by Monte Carlo simulation at each potential strike date, triggering additional stochastic processes. If banks with large portfolios are to calculate CVA across all instruments, including exotics, one solution is to approximate the full-scale model with something less computationally demanding but – hopefully – equally reliable.

There are a number of avenues available. When quants at UBS were trying to create a system to model, hedge and price counterparty credit exposure five years ago, they decided to adapt a method already used by trading desks to price American-style options. Called American Monte Carlo, the technique runs just a single inner scenario for each outer scenario and, by a process of regression, creates a valuation curve that can be used to numerically calculate the price distribution for the inner scenarios, thereby dramatically reducing the computation time.

“When you compute counterparty credit exposure, you need to generate Monte Carlo scenarios and calculate a price at each time point for each scenario. If this pricing itself requires Monte Carlo simulation, this becomes computationally unfeasible. But if you use American Monte Carlo you can generate scenarios and pricing at the same time, so the whole thing becomes possible,” says Giovanni Cesari, managing director and head of the portfolio quant group at UBS in London.

To run just our with-profit model takes an hour, even if we squeeze every bit of efficiency out of it. To run it 100,000 times would take 10 years,

The technique is also known as least-squares Monte Carlo, or least-squares regression, because the regression process minimises the sum of the squares of the errors between the value of the single inner simulations and full Monte Carlo stochastic runs. Cesari and his colleagues described their method in a book in 2009 and have subsequently implemented it for CVA, debit value adjustment (DVA) and limits across the majority of the bank’s book. “American Monte Carlo is a key technique in UBS’s approach to counterparty credit risk,” says Cesari.

UBS is not the only one taking this approach to the nested stochastic problem thrown up by CVA calculations. Munich-based real estate and public finance specialist Deutsche Pfandbriefbank is implementing American Monte Carlo for the CVA of all linear and non-linear instruments. “The benefit we see with American Monte Carlo is that we treat all instruments the same in our CVA calculations and can include netting and projected collateral postings for portfolios of derivatives,” says Roland Stamm, head of risk methods and valuation at the bank.

Deutsche Pfandbriefbank is implementing a CVA software application from New York-based analytics specialist Numerix, with the aim of calculating CVA in real time for each of the bank’s counterparties. Steve O’Hanlon, chief operating officer of Numerix, says American Monte Carlo is the only computationally effective method for calculating CVA for exotic instruments, and is usually the most effective method for non-linear vanilla instruments as well. As Cesari of UBS points out, although faster methods could be available for linear instruments, CVA is a portfolio measure and therefore requires a standard process across all instruments.

“You cannot compute CVA using a different model for each different type of trade and add up the results – you have to take the portfolio and compute the whole thing together,” says Cesari. “That requires a model that is sophisticated enough to give you good results, but also simple enough to cover all asset classes. This is a big challenge and one that American Monte Carlo can deal with.”

Several other risk technology suppliers, such as New Jersey-based Quantifi and Pennsylvania-based SunGard, also incorporate American Monte Carlo into their CVA and counterparty credit risk applications.

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