In this research paper, Drs. Alexandre Antonov, Serguei Issakov and Serguei Mechkov generalize the American Monte Carlo method to efficiently calculate future values (or exposures) of derivatives using an arbitrage-free model.

Specifically, they present efficient calculations of the portfolio values (exposure) in a self-consistent way using an arbitrage-free model that is calibrated to both implied market and real-world projections. They propose a new algorithmic method of simulation of exposures (distributions of future values) based on an iterative backward induction, a generalization of backward induction, especially attractive for exotic portfolios.

Backward Induction for Future Values

  • The paper applies this generalization to a simulation of exposures (distributions of future values) in the contexts of:
  • Various valuation adjustments (XVAs) due to counterparty risk, funding, capital, etc.,
  • Calculation of risk measures that use averages of future values, such as VAR and expected shortfall for market risk, and PFE EPE/ENE, etc. for counterparty risk.
  • Scenario generation, also in real-world measure.

Overall, highlights of this article include the generalization of the American / Least Square Monte Carlo method to compute the full future value – which we call Observation Value – by backward induction. The Observation Value accounts for all scenarios, including those on which exercises do occur, i.e. scenarios on which the instrument changes.

Complete the form to download this complimentary whitepaper, “Backward Induction for Future Values”

Authors: Dr. Alexandre Antonov,Dr. Serguei Issakov, and Dr. Serguei Mechkov

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