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Estimating the instantaneous volatility and covariance of risky assets

Author

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  • Marc Chesney
  • Robert J. Elliott

Abstract

Using the Mihlstein approximation for solutions to stochastic differential equations and the stochastic calculus an estimate for the volatility is obtained. The estimate is also valid for stochastic, Markov, volatilities. If the process has jumps, these reduce the previous estimate. The instantaneous covariance of two risky assets is also calculated.

Suggested Citation

  • Marc Chesney & Robert J. Elliott, 1995. "Estimating the instantaneous volatility and covariance of risky assets," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(1), pages 51-58, March.
    • Handle: RePEc:wly:apsmda:v:11:y:1995:i:1:p:51-58
    DOI: 10.1002/asm.3150110107
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    Cited by:

    1. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez, 2019. "Stochastic Brennan–Schwartz Diffusion Process: Statistical Computation and Application," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    2. Ahmed Nafidi & Ghizlane Moutabir & Ramón Gutiérrez-Sánchez & Eva Ramos-Ábalos, 2020. "Stochastic Square of the Brennan-Schwartz Diffusion Process: Statistical Computation and Application," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 455-476, June.
    3. Maxim Bouev & Ilia Manaev & Aleksei Minabutdinov, 2013. "Finding the Nearest Valid Covariance Matrix: An FX Market Case," EUSP Department of Economics Working Paper Series Ec-07/13, European University at St. Petersburg, Department of Economics.

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