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), including Funding Value Adjustment (FVA) and other XVA adjustments.

“Quantitatively all of these measures – RWA, CCE such as Potential Future Exposure (PFE) and XVA, as well as Economic Capital calculations by insurance firms are linked to the price and exposure distribution at future time horizons. This requires portfolio level Monte Carlo based simulations capable of producing risk neutral pricing at future time horizons along real world scenarios,” said Dr. Serguei Issakov SVP, Global Head of Quantitative Research, Quantitative Research & Development. “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.”

The backward American Monte Carlo based exposure approach has emerged as a much more efficient method than the Nested Simulation based exposure approach (also known as Brute Force, Monte Carlo-on-Monte Carlo, or Stochastic-on-Stochastic) as it leverages the same algorithm for pricing and exposures. However in leveraging American Monte Carlo, backward pricing has remained a challenge especially for path dependent instruments; and also when running risk neutral pricing on top of real world scenarios.

Las Vegas Monte Carlo with Resampling: Real World Algorithmic Exposures

Its latest research ‘Backward induction for future values’ Numerix uses its Algorithmic Exposure method in the backward (American) Monte Carlo to define efficient calculations of portfolio future values calibrated to both implied market and real world historical data. Using these calculations a new algorithmic method of simulation of exposures (distributions of the future values) was proposed based on an iterative backward induction.

“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,” said Dr. Alexander Antonov, SVP of Quantitative Research, Quantitative Research & 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.”

This 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, also in real world measure.

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.

Dr. Antonov continues: “The Las Vegas Monte Carlo and resampling based algorithmic exposure is a powerful tool for computing risk factors in both risk neutral and real world measures. 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.”

For a deeper understanding of this topic download the on-demand webinar: Real World Algorithmic Exposure: An Innovative New Approach for Nested Simulations.