Nonparametric Finance

Chapter 1Introduction

Nonparametric function estimation has many useful applications in quantitative finance. We study four areas of quantitative finance: statistical finance, risk management, portfolio management, and pricing of securities.¹

A main theme of the book is to study quantitative finance starting only with few modeling assumptions. For example, we study the performance of nonparametric prediction in portfolio selection, and we study the performance of nonparametric quadratic hedging in option pricing, without constructing detailed models for the markets. We use some classical parametric methods, such as Black–Scholes pricing, as benchmarks to provide comparisons with nonparametric methods.

A second theme of the book is to put emphasis on the study of economic significance instead of statistical significance. For example, studying economic significance in portfolio selection could mean that we study whether prediction methods are able to produce portfolios with large Sharpe ratios. In contrast, studying statistical significance in portfolio selection could mean that we study whether asset returns are predictable in the sense of the mean squared prediction error. Studying economic significance in option pricing could mean that we study whether hedging methods are able to well approximate the payoff of the option. In contrast, studying statistical significance in option pricing could mean that we study the goodness-of-fit of our underlying model for asset prices. Studying ...