Analysis of Investor Expectations Using Entropy Optimization Methods

• Main Author: Fernandes, Ana Sofia Pedrosa
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-2022
• Subjects: Arbitrage; Brownian motion; Derivatives; Economics; Entropy; Finance; Interest rates; Investments; Investors; Normal distribution; Probability distribution; Put & call options; Securities prices; Statistics; Volatility
• ISBN: 9798383842294

This paper aims to estimate a risk-neutral density function through option prices, by using entropy optimization methods. In their most basic form, these are methods aiming to maximize entropy subject to given constraints, allowing to obtain the least committal density with information not available in those constraints. These constraints result from the fact that option prices are directly related to payoff moments of the underlying asset. To ensure the applicability of one of these methods, we propose a careful selection of the option prices based on open interest data. To our knowledge, this feature is new in the context of entropy optimization methods. In order to test the reliability of these methods, we used simulated data from Black-Scholes-Merton and Heston models. Furthermore, we used data from S&P500 and VIX indexes and Microsoft company.Additionally, in order to try to extract relevant information regarding the market sentiment, we analyzed the mean, variance, skewness, and kurtosis for the estimated risk-neutral density functions obtained from market data.We propose an indicator that allows us to compare the risk-neutral density estimate in a given day to that of the previous day, verifying if there was a significant change. This indicator is based on the comparison of the current day’s density, obtained from the entropy maximization problem, and the density obtained by minimizing the cross-entropy with respect to the previous day. This indicator, as far as the authors know, is a new measure of the changes in the risk-neutral density estimates.