We study applications of nonparametric function estimation into risk management, portfolio management, and option pricing.

The methods of nonparametric function estimation have not been commonly used in risk management. The scarcity of data in the tails of a distribution makes it difficult to utilize the methods of nonparametric function estimation. However, it has turned out that some semiparametric methods are able to improve purely parametric methods.

Academic research has paid less attention to portfolio selection, as compared to the attention that has been paid to risk management and option pricing. We study applications of nonparametric prediction methods to portfolio selection. The use of nonparametric function estimation to reach practical financial decisions is an important part of machine learning.

Option pricing might be the most widely studied part of quantitative finance in academic research. In fact, the birth of modern quantitative finance is often dated to the 1973 publication of the Black–Scholes option pricing formula. Option pricing has been dominated by parametric methods, and it is especially interesting to provide some insights of nonparametric function estimation into option pricing.

The book is suitable for mathematicians and statisticians who would like to know about applications of mathematics and statistics into finance. In addition, the book is suitable for graduate students, researchers, and practitioners of quantitative finance who would like to study some underlying mathematics of finance, and would like to learn new methods. Some parts of the book require fluency in mathematics.

Klemelä (2014) is a book that contains risk management (volatility prediction and quantile estimation) and it describes methods of nonparametric regression, which can be applied in portfolio selection. In this book, we cover those topics and also include a part about option pricing.

The chapters are rather independent studies of well-defined topics. It is possible to read the individual chapters without a detailed study of the previous material.

The research in the book is reproducible, because we provide R-code of the computations. It is my hope, that this makes it easier for students to utilize the book, and makes it easier for instructors to adapt the material into their teaching.

The web page of the book is available in http://jussiklemela.com/statfina/.

Jussi Klemelä

Helsinki, Finland
June 2017