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