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Maximum Entropy in Option Pricing: A Convex‐Spline Smoothing Method

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  • Weiyu Guo

Abstract

Applying the principle of maximum entropy (PME) to infer an implied probability density from option prices is appealing from a theoretical standpoint because the resulting density will be the least prejudiced estimate, as “it will be maximally noncommittal with respect to missing or unknown information.”1 Buchen and Kelly (1996) showed that, with a set of well‐spread simulated exact‐option prices, the maximum‐entropy distribution (MED) approximates a risk‐neutral distribution to a high degree of accuracy. However, when random noise is added to the simulated option prices, the MED poorly fits the exact distribution. Motivated by the characteristic that a call price is a convex function of the option's strike price, this study suggests a simple convex‐spline procedure to reduce the impact of noise on observed option prices before inferring the MED. Numerical examples show that the convex‐spline smoothing method yields satisfactory empirical results that are consistent with prior studies. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:819–832, 2001

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  • Weiyu Guo, 2001. "Maximum Entropy in Option Pricing: A Convex‐Spline Smoothing Method," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 21(9), pages 819-832, September.
    • Handle: RePEc:wly:jfutmk:v:21:y:2001:i:9:p:819-832
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    Cited by:

    1. Salazar Celis, Oliver & Liang, Lingzhi & Lemmens, Damiaan & Tempère, Jacques & Cuyt, Annie, 2015. "Determining and benchmarking risk neutral distributions implied from option prices," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 372-387.
    2. Bogdan Negrea & Bertrand Maillet & Emmanuel Jurczenko, 2002. "Revisited Multi-moment Approximate Option," FMG Discussion Papers dp430, Financial Markets Group.
    3. Christopher Bose & Rua Murray, 2014. "Maximum Entropy Estimates for Risk-Neutral Probability Measures with Non-Strictly-Convex Data," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 285-307, April.

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