Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Article

The Maximum Entropy Distribution of an Asset Inferred from Option Prices

  • Peter W. Buchen (a1) and Michael Kelly (a2)

Abstract

This paper describes the application of the Principle of Maximum Entropy to the estimation of the distribution of an underlying asset from a set of option prices. The resulting distribution is least committal with respect to unknown or missing information and is, hence, the least prejudiced. The maximum entropy distribution is the only information about the asset that can be inferred from the price data alone. An extension to the Principle of Minimum Cross-Entropy allows the inclusion of prior knowledge of the asset distribution. We show that the maximum entropy distribution is able to accurately fit a known density, given simulated option prices at different strikes.

Copyright

COPYRIGHT: © School of Business Administration, University of Washington 1996

References

Hide All
Agmon, N.; Alhassid, Y.; and Levine, R. D.. “An Algorithm for Determining the Lagrange Parameters in the Maximal Entropy Formalism.” In The Maximum Entropy Formalism, Levine, R. D. and Tribus, M., eds. Cambridge, MA: MIT Press (1981), 207–209.
Amin, K. I., and Ng, V. K.. “Option Valuation with Systematic Stochastic Volatility.” Journal of Finance, 48 (1993), 881–910.
Breeden, D. T., and Litzenberger, R. H.. “Price of State-Contingent Claims Implicit in Option Prices.” Journal of Business, 51 (1978), 621–651.
Brennan, M. “The Pricing of Contingent Claims in Discrete-Time Models.” Journal of Finance, 34 (1979), 53–68.
Cover, T. M., and Joy, T. A.. Elements of Information Theory. New York, NY: John Wiley and Sons (1991).
Derman, E., and Kani, I.. “Riding on a Smile.” Risk, 7 (02 1994), 32–39.
Dupire, B. “Pricing and Hedging with Smiles.” Risk, 7 (01 1994), 18–20.
Derman, E., and Kani, I.. “Arbitrage Pricing with Stochastic Volatility.” Working Paper, Proceedings of AFFI Conference, Paris (06 1992).
Jarrow, R., and Rudd, A.. “Approximate Option Valuation for Arbitrary Stochastic Processes.” Journal of Financial Economics, 10 (1982), 347–369.
Jaynes, E. T. “Information Theory and Statistical Mechanics.” Physics Reviews, 106 (1957), 620–630.
Jaynes, E. T. “Where do We Stand on Maximum Entropy?” In The Maximum Entropy Formalism, Levine, R. D. and Tribus, M., eds. Cambridge, MA: MIT Press (1979), 115–118.
Jaynes, E. T. “On the Rationale of Maximum-Entropy Methods.” Proceedings of the IEEE, 70 (1982), 939–952.
Longstaff, F. A. “Option Pricing and the Martingale Restriction.” Finance Working Paper No. 8–94, Univ. of California (05 1994).
Rubinstein, M. “Implied Binomial Tree.” Finance Working Paper No. 232, Univ. of California (01 1994).
Shannon, C. E. “The Mathematical Theory of Communication.” Bell Systems Technical Journal, 27 (1948), 379–423.
Shimko, D. “Bounds of Probability.” Risk, 6 (1990), 33–37.

Related content

Powered by UNSILO

The Maximum Entropy Distribution of an Asset Inferred from Option Prices

  • Peter W. Buchen (a1) and Michael Kelly (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.