Decomposing the Option Pricing Problem : Estimating the Causal Factors: Interest Rates, Dividends, and Risk-Neutral Probabilities

Abstract: The financial markets have an essential role in society. Further, these markets are constantly evolving. Therefore, models and methods have to be developed and adapted to the new market conditions to be useful for decisions. This dissertation contributes to model and method developments by adapting them to new financial market functions by utilizing new possibilities within data and computation. The tools and techniques are from the field of financial engineering, including applied mathematics, computer science, and economic theory.The financial markets are important and complex, with many different intertwined factors. In this dissertation, one part of the complicated system is studied: the pricing of equity index options. It is impossible to understand all the connections between the financial factors. However, it is possible to observe the effects of the factors, which are asset prices. The same causal factors determine the prices of different traded assets. Hence, it is possible to understand and estimate the factors by studying the asset prices. The theme studied in the dissertation is the estimation of the factors that affect the equity index options. The three causal factors estimated in the dissertation are the interest rates (time values), dividend payments, and risk-neutral probabilities expressed as model parameters.The estimation of the causal factors is decomposed into separate inverse problems for interest rates and dividends, which are independent of the others, and a problem for the risk-neutral probabilities where the two other factors have been fixed. Further, the three causal factors are different, but the methods used to estimate them share the same idea. A financial relationship isolates one factor, and mathematical models are used to formulate an estimation problem (inverse problem). The estimation is performed on intraday data observed in the market. The dissertation contributes primarily to the development of three areas of financial engineering: model, data, and methodology, where the most focus has been on the last.The model development is a novel way of modeling dividends as a term structure, complementing the traditional modeling approach that also is used in the dissertation. The term structure is similar to the typical modeling approach of interest rates. This new way of modeling allows more homogeneous modeling with the interest rates, which could improve option pricing. The data development is that the method in the dissertation is based on and adapted to high-frequent intraday data.The focus of the dissertation is the method. A general principle of the dissertation is that the methods are more data-driven than previous methods in the literature. This principle, combined with high-frequency data, has made it possible to weaken the necessary assumptions and generalize the estimation methods. The interest rates and traditional dividends are estimated with weighted least squares, where the weights are determined with a scheme that utilizes the high data frequency. These methods generalize and improve the ordinary least squares approach previously used in the literature. The novel modeling of the dividend term structure is a generalization of the dividend modeling and is accompanied by an estimation method. The method is based on formulating an optimization problem that combines repricing of market data and regularization. The former is based on the same high-frequency data, while the latter is based on historical data. Further-more, the risk-neutral probability factor estimation problem is formulated as a classic calibration problem, where model parameters are calibrated to fit the observed market data. The contribution of the dissertation is the algorithm used to solve the optimization problem.