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Explicit Formulae For Parameters Of Stochastic Models Of A Discounted Equity Index Using Maximum Likelihood Estimation With Applications

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  • K. FERGUSSON

    (Centre for Actuarial Studies, University of Melbourne, Carlton VIC 3059, Australia)

Abstract

A discounted equity index is computed as the ratio of an equity index to the accumulated savings account denominated in the same currency. In this way, discounting provides a natural way of separating the modeling of the short rate from the market price of risk component of the equity index. In this vein, we investigate the applicability of maximum likelihood estimation to stochastic models of a discounted equity index, providing explicit formulae for parameter estimates. We restrict our consideration to two important index models, namely the Black–Scholes model and the minimal market model of Platen, each having an explicit formula for the transition density function. Explicit formulae for estimates of the model parameters and their standard errors are derived and are used in fitting the two models to US data. Further, we demonstrate the effect of the model choice on the no-arbitrage assumption employed in risk neutral pricing.

Suggested Citation

  • K. Fergusson, 2017. "Explicit Formulae For Parameters Of Stochastic Models Of A Discounted Equity Index Using Maximum Likelihood Estimation With Applications," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 1-31, June.
    • Handle: RePEc:wsi:afexxx:v:12:y:2017:i:02:n:s2010495217500105
    DOI: 10.1142/S2010495217500105
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    References listed on IDEAS

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    1. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
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    13. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Kevin Fergusson, 2020. "Forecasting inflation using univariate continuous‐time stochastic models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 37-46, January.

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