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3 results

  • 8 - Market Risk Models

  • Mary R. Hardy, University of Waterloo, Ontario, David Saunders, University of Waterloo, Ontario
  • Book:
    Quantitative Enterprise Risk Management
    Published online:
    28 July 2022
    Print publication:
    05 May 2022, pp 227-261

  • Summary

    We review the difference between real-world and risk-neutral processes. We illustrate asset processes using two years of daily returns from the S\&P 500 stock index, and with 30 years of monthly data from the S\&P/TSX (Toronto Stock Exchange) stock index. We describe three models for modelling asset prices in discrete time: the independent lognormal model, the GARCH model, and the regime-switching lognormal model. We describe how the models are fitted to data, and briefly discuss how to choose between models.

  • Continuous-Time Skewed Multifractal Processes as a Model for Financial Returns

  • Part of
  • Emmanuel Bacry, Laurent Duvernet, Jean-François Muzy
  • Journal:
    Journal of Applied Probability / Volume 49 / Issue 2 / June 2012
    Published online by Cambridge University Press:
    04 February 2016, pp. 482-502
    Print publication:
    June 2012
    • Article
      • You have access
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  • We present the construction of a continuous-time stochastic process which has moments that satisfy an exact scaling relation, including odd-order moments. It is based on a natural extension of the multifractal random walk construction described in Bacry and Muzy (2003). This allows us to propose a continuous-time model for the price of a financial asset that reflects most major stylized facts observed on real data, including asymmetry and multifractal scaling.

  • An Exponential Continuous-Time GARCH Process

  • Part of
  • Stephan Haug, Claudia Czado
  • Journal:
    Journal of Applied Probability / Volume 44 / Issue 4 / December 2007
    Published online by Cambridge University Press:
    14 July 2016, pp. 960-976
    Print publication:
    December 2007
    • Article
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  • In this paper we introduce an exponential continuous-time GARCH(p, q) process. It is defined in such a way that it is a continuous-time extension of the discrete-time EGARCH(p, q) process. We investigate stationarity, mixing, and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous-time GARCH(p, p) model.