JURCZENKO Emmanuel

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The research work carried out in this thesis is essentially aimed at detecting regime and behavioral changes of agents through options markets. Indeed, option prices allow us to deconstruct and analyze the behavior of agents in financial markets in order to obtain a better understanding of their expectations and preferences. This information resides in particular in the valuation method of these conditional contracts. It is indeed possible to extract from option prices an implicit probability density, known as risk neutral, that reflects agents' expectations about the future evolution of the underlying asset. In the first part of this thesis, we classify the different approaches used in the literature for this purpose. We also show the advantages and disadvantages of each of them. The second part of the thesis is devoted to the description of a new non-para metric method based on Padé approximants. This method of extracting the risk-neutral density does not require any assumption about the process followed by the returns of the underlying asset. It also has the advantage of respecting the no-arbitrage constraints and offers the possibility to differentiate locally the treatment of the initial information according to common characteristics. Nevertheless, the non-parametric extraction of the neutral risk density also has limitations due to the different sources of noise that alter the information contained in the option prices. In the third part, we study the components of this noise while simulating their respective effects on the extracted information. Among these sources of information distortion, we focus on the bid-ask spread, which is omnipresent in the markets. Thus, the fourth part, in which we introduce the notion of discontinuity cost, allows us to complete the recent literature on the typology of micro-structure phenomena impacting the bid-ask spread applied on options markets. Our contribution in this area also modifies the symmetry that is often assumed in the literature between the bid and ask prices in options markets. Finally, this microeconomic phenomenon studied on high-frequency data also allows us to state robust hypotheses regarding the location of a fair price for each option. On this basis, we have proposed an innovative approach, based on the supervised learning technique of support vector machines (SVM), which allows us to take into account this asymmetry in our regression of the fair price on the bid-ask spreads quoted continuously on the options markets. The last part of this thesis is devoted to the empirical application of our nonparametric method and to the interpretation of the extracted information. First, we explain how Padé's multi-point approximants can be implemented on a set of simulated and noiseless option prices. We then use real data to show that there is a clear relationship between the implied volatility computed from the risk-neutral density and the realized volatility of the underlying asset in the short run. However, the relationship between the higher order moments extracted from option prices (in other words, the skewness and kurtosis implied by the risk-neutral density) and those that can be computed directly from the realized returns of the underlying asset does not seem to be as obvious or even non-existent.

Our work aims to present, in a unified framework, the theoretical foundations and properties of four-time asset pricing and option pricing models. In fact, this work combines different fields of analysis: decision theory under uncertainty, portfolio choice theory, financial asset pricing and option pricing. In the first part, we study the decision foundations and properties of equilibrium models of financial asset prices at four moments. Contrary to what is usually assumed in the framework of allocation and valuation models, we show that the choice of a Taylor series expansion stopped at order four has no particular theoretical superiority over a quartic polynomial utility function when it comes to justifying a mean-variance-asymmetry-kurtosis decision criterion. The study of the general properties of the frontier of mean-variance-asymmetry-kurtosis efficient portfolios allows us to extend the Sharpe-Lintner-Mossin asset pricing model to four points in time with or without a non-risky asset. In the second part we study the theoretical foundations and properties of semi-parametric pricing models of European call options at four points in time. This allows us to correct the original model formulation of Corrado and Su (1996-b and 1997-b ) for an important economic and financial error.