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

Download Numerix Research Paper

Complete the form below to download this complimentary research paper.

Select Form: 

Form #5: Research

Keep me informed of future research from Numerix:

Sign me up to receive "Derivative Insights & Innovations" monthly newsletter by Numerix:

* Required fields
product collateral

Numerix Oneview Graph Framework Fact Sheet

on-demand webinar

Tipping Points for Legacy Risk System Replacement: The CRO View

conference presentation

Margin Valuation Adjustments

newsletter issue - Nov 9, 2017

Derivative Insights & Innovations - November 2017 Issue

video blog

Technology in Fixed Income Trading

content collection

NEXT 365

analyst report, white paper

Aite: Risk System Replacement Pitfalls and Lessons Learned

analyst report

Greenwich Associates - The Technology to Succeed in Fixed-Income Trading

newsletter issue - Oct 12, 2017

Derivative Insights & Innovations - October 2017 Issue

conference presentation

Pricing and Risk Analytics with the MATLAB-Numerix Interface

video blog

Fear of Fintech & Cybersecurity

video blog

What Is “Fintech”?