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2019 | Buch

Derivatives Kapitel lesen Erstes Kapitel lesen

Statistics of Financial Markets

An Introduction

verfasst von: Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner

Verlag: Springer International Publishing

Buchreihe : Universitext

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Now in its fifth edition, this book offers a detailed yet concise introduction to the growing field of statistical applications in finance. The reader will learn the basic methods for evaluating option contracts, analyzing financial time series, selecting portfolios and managing risks based on realistic assumptions about market behavior. The focus is both on the fundamentals of mathematical finance and financial time series analysis, and on applications to specific problems concerning financial markets, thus making the book the ideal basis for lectures, seminars and crash courses on the topic. All numerical calculations are transparent and reproducible using quantlets.

For this new edition the book has been updated and extensively revised and now includes several new aspects such as neural networks, deep learning, and crypto-currencies. Both R and Matlab code, together with the data, can be downloaded from the book’s product page and the Quantlet platform.

The Quantlet platform quantlet.de, quantlet.com, quantlet.org is an integrated QuantNet environment consisting of different types of statistics-related documents and program codes. Its goal is to promote reproducibility and offer a platform for sharing validated knowledge native to the social web. QuantNet and the corresponding Data-Driven Documents-based visualization allow readers to reproduce the tables, pictures and calculations inside this Springer book.

“This book provides an excellent introduction to the tools from probability and statistics necessary to analyze financial data. Clearly written and accessible, it will be very useful to students and practitioners alike.”

Yacine Ait-Sahalia, Otto Hack 1903 Professor of Finance and Economics, Princeton University

Inhaltsverzeichnis

Frontmatter

Option Pricing

Frontmatter
Chapter 1. Derivatives
Abstract
Classic financial mathematics deals first and foremost with basic financial instruments such as stocks, foreign currencies and bonds.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 2. Introduction to Option Management
Abstract
In this section we consider the fundamental notion of no-arbitrage. An arbitrage opportunity arises if it is possible to make a riskless profit.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 3. Basic Concepts of Probability Theory
Abstract
Thanks to Newton’s laws, dropping a stone from a height of 10 m, the point of time of its impact on the ground is known before executing the experiment.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 4. Stochastic Processes in Discrete Time
Abstract
A stochastic process or random process consists of chronologically ordered random variables {Xt; t ≥ 0}. For simplicity we assume that the process starts at time t = 0 in X0 = 0.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 5. Stochastic Integrals and Differential Equations
Abstract
This chapter provides the tools needed for option pricing. The field of stochastic processes in continuous time, which are defined as solutions of stochastic differential equations, has an important role to play.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 6. Black–Scholes Option Pricing Model
Abstract
Simple, generally accepted economic assumptions are insufficient to develop a rational option pricing theory.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 7. Binomial Model for European Options
Abstract
A large range of options exist for which the boundary conditions of the Black–Scholes differential equation are too complex to solve analytically, an example being the American option.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 8. American Options
Abstract
Pricing American options is a more complex task than for European options since they can be exercised any time up to expiry. The moment the holder chooses to exercise option depends on the spot price of the underlying asset St.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 9. Exotic Options
Abstract
There is a multitude of complex, so-called exotic options, which are mainly used in OTC (over the counter) trading to meet the special needs of institutional investors. The most important types of exotic options are:
  • Compound Options
  • Chooser Options
  • Barrier Options
  • Asian Options
  • Lookback Options
  • Cliquet Options
  • Basket Options
In contrast, ordinary puts and calls, no matter whether European or American style, are frequently called plain vanilla options.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 10. Interest Rates and Interest Rate Derivatives
Abstract
The interest rate derivatives market is the largest derivatives market in the world. Mostly traded OTC, the interest rate securities are extremely popular especially among large institutional investors. Thus, the valuation of these instruments has been a major challenge for both practitioners and academics. Pricing interest rate derivatives fundamentally depends on the term structure of interest rates.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner

Statistical Models of Financial Time Series

Frontmatter
Chapter 11. Introduction: Definitions and Concepts
Abstract
Financial markets can be regarded from various points of view. Firstly there are economic theories which make assertions about security pricing; different economic theories exist in different markets (currency, interest rates, stocks, derivatives, etc.).
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 12. ARIMA Time Series Models
Abstract
In this chapter we will deal with classic, linear time series analysis. At first we will define the general linear process.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 13. Time Series with Stochastic Volatility
Abstract
In the previous chapters we have already discussed that volatility plays an important role in modelling financial systems and time series. Unlike the term structure, volatility is unobservable and thus must be estimated from the data.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 14. Long Memory Time Series
Abstract
Empirical studies involving economic variables such as price level, real output and nominal interest rates have been shown to exhibit some degree of persistence. Moreover, findings across several asset markets have revealed a high persistence of volatility shocks and that over sufficiently long periods of time the volatility is typically stationary with “mean-reverting” behaviour.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 15. Non-Parametric and Flexible Time Series Estimators
Abstract
With the analysis of (financial) time series, one of the most important goals is to produce forecasts. Using past data one can argue about the future mean, the future volatility and so on; however, a flexible method of producing such estimates will be introduced in this chapter.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner

Selected Financial Applications

Frontmatter
Chapter 16. Value at Risk and Backtesting
Abstract
The Value-at-Risk (VaR) is probably the most known measure for quantifying and controlling the risk of a portfolio. The establishment of VaR is of central importance to a credit institute, since it is the basis for a regulatory notification technique and for required equity investments.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 17. Copulae and Value-at-Risk
Abstract
The capital requirement from financial institutions is based on the amount of risk carried in their portfolios.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 18. Statistics of Extreme Risks
Abstract
When we model returns using a GARCH process with normally distributed innovations, we have already taken into account the second stylised fact (see Chap. 13).
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 19. Neural Networks and Deep Learning
Abstract
Deep learning is a group of optimisation methods for artificial neural networks. The field consists of three major branches.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 20. Volatility Risk of Option Portfolios
Abstract
In this chapter we analyse the principal factors in the dynamic structure of implied volatility at the money (ATM).
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 21. Nonparametric Estimators for the Probability of Default
Abstract
The estimation of the probability of default based on information on the individual customer or the company is an important part of credit screening, i.e. judging the credit standing.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 22. Credit Risk Management and Credit Derivatives
Abstract
Credit risk management is an important issue in banking. In this chapter we give an overview of the models for calculating the default risk exposure of a credit portfolio.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Chapter 23. Financial Econometrics of Cryptocurrencies
Abstract
This chapter is based partly on the texts provided by Elendner et al. (2018) Handbook of digital finance and financial inclusion: Cryptocurrency, FinTech, InsurTech, Regulation, ChinaTech, Mobile Security, and Distributed Ledger. 1st Edition and Chen et al. (2017) Handbook of digital finance and financial inclusion: Cryptocurrency, FinTech, InsurTech, Regulation, ChinaTech, Mobile Security, and Distributed Ledger. 1st Edition. As the economy is becoming more and more digital, the role of digital assets in investment decisions will also grow.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner
Backmatter
Metadaten
Titel
Statistics of Financial Markets
verfasst von
Jürgen Franke
Wolfgang Karl Härdle
Christian Matthias Hafner
Copyright-Jahr
2019
Electronic ISBN
978-3-030-13751-9
Print ISBN
978-3-030-13750-2
DOI
https://doi.org/10.1007/978-3-030-13751-9