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A more informative estimation procedure for the parameters of a diffusion process

Author

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  • Basso, A.
  • Pianca, P.

Abstract

The estimation procedures for the parameters of a diffusion process with constant coefficients have mainly focused on volatility. Nevertheless, even if the knowledge of the volatility alone suffices to compute the Black and Scholes option prices, other financial application models assume that the price dynamics follows a log-normal process and requires the knowledge of both parameters. On the other hand, while the usual ML estimator of volatility gives satisfactory results, the estimation of drift is much less accurate; moreover, the drift-estimated value highly depends on the phases of the business cycle included in the sample data. This contribution explicitly imposes a risk aversion or risk neutral assumption into the ML estimation procedure and makes a constrained maximization of the sample likelihood function. The aim is twofold: to obtain estimated values which are consistent with a widely accepted assumption and use the risk aversion constraint in order to improve the accuracy of the estimates.

Suggested Citation

  • Basso, A. & Pianca, P., 1999. "A more informative estimation procedure for the parameters of a diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 45-53.
    • Handle: RePEc:eee:phsmap:v:269:y:1999:i:1:p:45-53
    DOI: 10.1016/S0378-4371(99)00078-3
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    References listed on IDEAS

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    1. Goldenberg, David H., 1991. "A unified method for pricing options on diffusion processes," Journal of Financial Economics, Elsevier, vol. 29(1), pages 3-34, March.
    2. Goldenberg, David H. & Schmidt, Raymond J., 1996. "On Estimating the Expected Rate of Return in Diffusion Price Models with Application to Estimating the Expected Return on the Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(4), pages 605-631, December.
    3. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    4. Antonella Basso & Paolo Pianca, 1997. "Decreasing Absolute Risk Aversion and Option Pricing Bounds," Management Science, INFORMS, vol. 43(2), pages 206-216, February.
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