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2023 | Book

Basic Products and Interest Calculations Read chapter Read first chapter

The Art of Quantitative Finance Vol.1

Trading, Derivatives and Basic Concepts

Author: Gerhard Larcher

Publisher: Springer International Publishing

Book Series : Springer Texts in Business and Economics

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This textbook offers an easily understandable introduction to the fundamental concepts of financial mathematics and financial engineering. The author presents and discusses the basic concepts of financial engineering and illustrates how to trade and to analyze financial products with numerous examples. Special attention is given to the valuation of basic financial derivatives. In the final section of the book, the author introduces the Wiener Stock Price Model and the basic principles of Black-Scholes theory. The book’s aim is to introduce readers to the basic techniques of modern financial mathematics in a way that is intuitive and easy to follow, and to provide financial mathematicians with insights into practical requirements when applying financial mathematical techniques in the real world.

Table of Contents

Frontmatter
1. Basic Products and Interest Calculations
Abstract
We give an introduction into basic financial products—like bonds, stocks, and stock indices—and into their basic properties. Specifically, we will study the S&P500 stock index in more detail. Further, we provide the basics of discrete and continuous compounding and we give an overview of the most important interest rate and swap rate benchmarks.
Gerhard Larcher
2. Derivatives and Trading in Derivatives, Basic Concepts and Strategies
Abstract
We define the basic types of derivatives, namely, European and American plain-vanilla call- and put-stock-options and futures and we discuss fundamental properties. We introduce the most basic option-strategies like straddles, protective puts, and covered calls. We discuss the question which type of investor is especially interested in which type of application of derivatives. We also give details on how to trade options and futures on an electronic trading platform and on margin requirements for short positions in derivatives.
Gerhard Larcher
3. Basics of Derivative Valuation
Abstract
We define frictionless markets and clarify what we mean by a “fair value” of a financial product in a frictionless market. Then we state and discuss the fundamental axiom in quantitative finance, the “no-arbitrage principle”. We give first applications of this NA principle and thereby derive the put-call-parity-equation and the formula for the fair price of futures. Finally, we provide the first steps towards the valuation of options: We define binomial stock-models, we give the formulas for the fair value of derivatives in such binomial models, and we show how hedging of derivatives in a binomial model is carried out.
Gerhard Larcher
4. The Wiener Stock Price Model and the Basic Principles of Black-Scholes Theory
Abstract
We give basic tools for the statistical analysis of financial data. Especially we introduce the basic parameters trend, volatility, and correlation for stocks. Then we motivate and derive the Wiener stock price model (geometric Brownian motion). Thereby we discuss the goals and the meaning of mathematical modeling in general. We then show that—if parameters are chosen in a suitable way—the binomial N-step-model converges to the Wiener model. As a consequence we derive the Black-Scholes formula, i.e. the formula for the fair price of derivatives over an underlying which follows a Wiener model. We extensively discuss this pricing formula for plain vanilla call and put options and for strategies built by combinations of these options. We define the “Greeks” (i.e., the derivations of the fair prices with respect to different parameters), and we discuss the Greeks for various examples in detail. Finally we explain how hedging derivatives in a Wiener model is carried out.
Gerhard Larcher
Metadata
Title
The Art of Quantitative Finance Vol.1
Author
Gerhard Larcher
Copyright Year
2023
Electronic ISBN
978-3-031-23873-4
Print ISBN
978-3-031-23872-7
DOI
https://doi.org/10.1007/978-3-031-23873-4