Numerix Adds 'Las Vegas Monte Carlo' Exposure Calculation to Analytics

A challenge since 2008 with the introduction Basel II and III, Solvency II insurance regulation and IFRS 13, financial institutions are required to hold capital and reserves sufficient to support their risks. The monitoring, hedging or optimization of risk has been compounded with the Risk Weighted Assets minimal capital requirement (RWA), Counterparty Credit Exposures (CCE) and Credit Value Adjustment (CVA) as well as Funding Value Adjustment (FVA) and related XVA adjustments.

“Quantitatively all of these measures are linked to the price and exposure distribution at future time horizons," says Dr. Serguei Issakov SVP, global head of quantitative research. "This requires portfolio level Monte Carlo based simulations capable of producing risk neutral pricing at future time horizons along real world scenarios. The challenge then becomes how to combine scenario generation – both in risk neutral and real world measures to obtain exposures along a given scenario at a future time horizon. For large portfolios of deals, these calculations can require billions of simulation paths and can take significant amounts of time.”

Backward Induction

Using iterative backward induction, the new method of simulation of exposures can be applied in the contexts of various valuation adjustments (XVA) accounting for counterparty risk, funding and capital, the calculation of risk measures that use averages of future values, such as VaR and expected shortfall for market risk, and PFE, EPE/ENE, for counterparty risk, scenario generation, and in real world measures.

“In our research we’ve generalized the backward induction to compute a future value of a derivative on real world scenarios that corresponds to the full instrument value on future dates with effects of exercises and triggers included,” says Dr. Alexander Antonov, SVP of quantitative research and development. “Referred to as the Las Vegas Monte Carlo method, this approach enables a much more efficient exposure of path dependent instruments especially options with early exercise optionality like Barriers, Bermudan Swaptions and Autocaps. Also for those instruments where option value is dependent on underlying fixings history like an Asian and Lookback option.”

To determine algorithmic exposure under real world measure a resampling technique may also be applied – essentially resampling of the price distribution on the future observation date. The Numerix resample algorithm obtains risk neutral pricing on real world scenarios based on backward Monte Carlo.

“The approach avoids the inefficiency of the Brute Force approach for simulation on real world economic scenarios and dramatically reduces computation times by using resampling to connect real world scenarios with American Monte Carlo," Antonov adds.