Applications of Eigensystem Analysis to Derivatives
and Portfolio Management

Abstract

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.