Applications of Eigensystem Analysis to Derivatives and Portfolio Management

Eigensystem structure plays the key role in principal component analysis (PCA). However, the application of it in high-frequency datasets is noticeably thin, especially for derivatives pricing. In my thesis, I will present the predictive power of eigenvalue/eigenvector analysis in several nancial markets. Performance of prediction based on eigenvalue/eigenvector structure shows the result that this methodology is reliable compared with traditional methodology. To verify the performance of eigensystem analysis in derivatives pricing, I select one of the most important nancial markets: the foreign exchange(FX) option market as datasets. The traditional pricing models for FX options are highly reliant on historical data, which leads to the dilemma that for those contracts with less liquidity investors nd it dicult to provide reliable guidance on price. I will present a brand-new model based on eigensystem analysis to provide accurate guidance for option pricing, especially in cases where the underlying asset is considered to be an illiquid currency pair. The importance of eigenvalues and eigenvectors structure in asset pricing will be explored in this thesis. The empirical study covers FX option contracts across deltas and maturities. The performance of eigensystem model are compared with other widely used models, results indicate that traditional models are outperformed in all selected underlying assets, maturities and deltas. In addition, I perform analysis of machine learning performance based on theFX market's empirical asset pricing problem. I demonstrate the advantage of machine learning in promoting the predictive power of eigensystem based on multiple predictors from the OTC market. Black-Scholes implied volatility is used as predictors for the eigenvalue error between market and our innovative eigensystem. I identify the regression tree algorithm's predictive gain with empirical study across contracts. The eect of currency pairs is numerical and sorted to generate an overview for global FX market structure. I also implement eigenstructure analysis based on the S&P500 market. I discover the convergence of rst principal component explanatory power. In order to generate the statistical summary for trend of principal components, I raise a set of measurements and thresholds to describe eigenvalue and eigenvector structure in market portfolios.