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Montecarlo simulation of long-term dependent processes: a primer

Author

Listed:
  • Carlos Leóm

    ()

  • Alejandro Reveiz

    ()

Abstract

As a natural extension to León and Vivas (2010) and León and Reveiz (2010) this paper briefly describes the Cholesky method for simulating Geometric Brownian Motion processes with long-term dependence, also referred as Fractional Geometric Brownian Motion (FBM). Results show that this method generates random numbers capable of replicating independent, persistent or antipersistent time-series depending on the value of the chosen Hurst exponent. Simulating FBM via the Cholesky method is (i) convenient since it grants the ability to replicate intense and enduring returns, which allows for reproducing well-documented financial returns’ slow convergence in distribution to a Gaussian law, and (ii) straightforward since it takes advantage of the Gaussian distribution ability to express a broad type of stochastic processes by changing how volatility behaves with respect to the time horizon. However, Cholesky method is computationally demanding, which may be its main drawback. Potential applications of FBM simulation include market, credit and liquidity risk models, option valuation techniques, portfolio optimization models and payments systems dynamics. All can benefit from the availability of a stochastic process that provides the ability to explicitly model how volatility behaves with respect to the time horizon in order to simulate severe and sustained price and quantity changes. These applications are more pertinent than ever because of the consensus regarding the limitations of customary models for valuation, risk and asset allocation after the most recent episode of global financial crisis.

Suggested Citation

  • Carlos Leóm & Alejandro Reveiz, 2011. "Montecarlo simulation of long-term dependent processes: a primer," Borradores de Economia 648, Banco de la Republica de Colombia.
  • Handle: RePEc:bdr:borrec:648
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    Cited by:

    1. Carlos León, 2012. "Implied probabilities of default from Colombian money market spreads: The Merton Model under equity market informational constraints," BORRADORES DE ECONOMIA 010075, BANCO DE LA REPÚBLICA.
    2. Carlos Léon, 2012. "Estimating financial institutions´ intraday liquidity risk: a Monte Carlo simulation approach," BORRADORES DE ECONOMIA 009441, BANCO DE LA REPÚBLICA.

    More about this item

    Keywords

    Montecarlo simulation; Fractional Brownian Motion; Hurst exponent; Long-term Dependence; Biased Random Walk. Classification JEL: C15; C53; C63; G17; G14.;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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