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.
Author(s): Gerhard Larcher
Series: Springer Texts in Business and Economics
Publisher: Springer
Year: 2023
Language: English
Pages: 531
City: Cham
Foreword
Acknowledgements
Preface to Volume I
About This Book
Contents
1 Basic Products and Interest Calculations
1.1 Basic Properties of Bonds
1.2 Example of a Bond
1.3 Issuance of a Bond and Initial Issue Price
1.4 Chart of the Bond and Factors Influencing Price Developments
1.5 Discrete and Continuous Interest Compounding
1.6 Continuous Compounding at a Time-Varying Interest Rate
1.7 Euribor, Libor, Swap Rates, and Key Interest Rates
1.8 Two Comments Regarding Loans: Calculation of Continuously Redeemable Loan Instalments as Well as Foreign Currency Loans and Interest Rate Parity Theory
1.9 Bond Yields
1.10 Forward Interest Rates
1.11 The Fair Value of a Future Payment, Discounting
1.12 The Fair Value of a Bond
1.13 Some Examples of Junk Bonds
1.14 Stock (Basics)
1.15 Stock Market Dynamics
1.16 Stock Indices
1.17 Trading in Indices Through Index Certificates
1.18 The ShortDAX and Index Certificates on the ShortDAX
1.19 The S&P500 Index
1.20 The S&P500 on the Black Monday of 19 October 1987
1.21 11 September 2001
1.22 The S&P500 Index Around 10 October 2008, Overnight Gaps
1.23 The ``Flash Crash'' on 6 May 2010
1.24 Price Forecasting and Run Analyses of Stock Prices and Index Prices
1.25 Notes on a Simple Trading Strategy by Signals Using Exponential Moving Averages
2 Derivatives and Trading in Derivatives, Basic Concepts and Strategies
2.1 What Is a Derivative?
2.2 European Plain-Vanilla Options, Definition and Basic Characteristics
2.3 American Options
2.4 Any Strategy Is Better than No Strategy and ``The Secretary Problem''
2.5 How Do You Trade Options? Trading Through a Bank
2.6 How Do You Trade Options? Trading Through an Electronic Trading Platform
2.7 Who Trades in Options? Long Positions in Call Options, Leverage
2.8 Who Trades in Options? Long Positions in Put Options, Protective Put
2.9 Who Trades in Options? Short Positions in Put Options, Selling Insurance, Put Spreads
2.10 Who Trades in Options? Short Positions in Call Options, Covered Call Strategies
2.11 Discount Certificates
2.12 Who Trades in Options? Long Straddle, Short Straddle
2.13 Relationship Between the Payoffs of Puts, Calls, and Underlying Asset
2.14 More Option Combinations
2.15 Margin Rules for Short Positions in (CBOE S&P500) Options
2.16 CBOE-Traded Options on the S&P500 Index, Market-Maker System, Settlement of SPX Options
2.17 Futures, Basic Characteristics, Trading, Margin
2.18 Long and Short Trades of Underlying Assets with Futures
2.19 The ``Euro-Bund Future''
2.20 More Comments on Futures Contracts (Rolling, Futures Options, Forwards)
References
3 Basics of Derivative Valuation
3.1 Frictionless Markets and the No-Arbitrage Principle
3.2 Application of the NA Principle: Put-Call Parity Equation
3.3 Simple Conclusions from the Put-Call Parity Equation
3.4 Another Application of the NA Principle: The ``Fair'' Strike Price of a Futures Contract (on a Dividend-Free/Cost-Free Underlying Asset)
3.5 Valuation of Futures for Underlying Assets with Payouts or Costs
3.6 The Put-Call Parity Equation for Underlying Assets with Payouts or Costs
3.7 Basics of Derivative Valuation and Pricing Models
3.8 The One-Step Binomial Model and Derivative Valuation in the One-Step Binomial Model: Part I
3.9 The One-Step Binomial Model and Derivative Valuation in the One-Step Binomial Model: Part II
3.10 Derivative Valuation in the One-Step Binomial Model: Discussion of Outcomes
3.11 A Brief Excursus on the Degree of Luck and Skill in Games
3.12 Fair Price of Derivatives in the Binomial Model on Underlying Assets with Payouts/Costs
3.13 The Two-step Binomial Model
3.14 Derivative Valuation in the Two-Step Binomial Model: Discussion of Results
3.15 Hedging and Arbitrage in the Two-Step Binomial Model
3.16 Numerical Example of How to Value and Hedge Derivatives and Execute Arbitrage Trades in a Two-Step Binomial Model
3.17 Derivative Valuation in the N-Step Binomial Model
3.18 Comments on the Valuation of Derivatives in the N-Step Binomial Model and an Example
3.19 Derivative Valuation in the N-Step Binomial Model on Underlying Assets with Payouts or Costs
Reference
4 The Wiener Stock Price Model and the Basic Principles of Black-Scholes Theory
4.1 Basic Tools for Analysing Real Stock Prices: Trend, Volatility, Distribution of Returns, Skewness, and Kurtosis
4.2 Basic Tools for Analysing Real Stock Prices: Covariances and Correlations
4.3 Basic Tools for Analysing Real Stock Prices: Autocorrelations of Stock Returns
4.4 What Does Mathematical Modeling Mean? What Is a Stock Price Model?
4.5 The Wiener Stock Price Model
4.6 Simulation of Stock Prices in the Wiener Model
4.7 Simulation of Two Correlated Stock Prices
4.8 Simulation of Several Correlated Stock Prices
4.9 Simulation of a Wiener Model for Given Initial and Final Values: The Brownian Bridge
4.10 Expectations, Variances, and Probability Distributions of Stock Prices in the Wiener Model
4.11 Approximation of the Wiener Model Through Binomial Models: Preliminary Remarks
4.12 Approximation of the Wiener Model Through Binomial Models: Preparation
4.13 The Central Limit Theorem
4.14 Approximation of the Wiener Model Through Binomial Models: The Proof (Sketch of Proof)
4.15 The Brownian Motion, Motivation, and Definition
4.16 The Brownian Motion: Basic Properties
4.17 The Wiener Model as a Geometric Brownian Motion and the Brownian Motion with Drift
4.18 The Black-Scholes Formula in the Wiener Model
4.19 The Fair Price of a European Call Option and a European Put Option in the Wiener Model
4.20 A (Very) Short History of the Black-Scholes Formula
4.21 Perfect Hedging in the Black-Scholes Model
4.22 Another Example of the Application of the Black-Scholes Formula and of Perfect Hedging as Well as Its Implementation in Discrete Hedging
4.23 Discretely Approximated Perfect Hedging for European Derivatives, Especially for European Call and Put Options
4.24 Detailed Discussion of the Black-Scholes Formula for European Call Options I (Dependence on S and t, Intrinsic Value, Fair Value)
4.25 Detailed Discussion of the Black-Scholes Formula for European Call Options II (Dependence on Volatility)
4.26 Detailed Discussion of the Black-Scholes Formula for European Call Options III (Dependence on Risk-Free Interest Rate)
4.27 Some Brief Remarks on the Use of the Black-Scholes Formula and Its Parameters r and σ
4.28 Program and Test: Valuation of Derivatives by Approximation Using an N-Step Binomial Model Where Volatility Is Correlated with the Price of the Underlying Asset
4.29 Break-Even for Call-Only Strategies
4.30 Analysis of the Black-Scholes Price of Put Options
4.31 Break-Even for Put-Only Strategies
4.32 Analysis of the Price Paths of a Few Other Basic Option Strategies: Short Iron Butterfly
4.33 Analysis of the Price Curves of a Few Other Basic Option Strategies: Naked Short Butterfly
4.34 Excursus: Brief Remark on the ``Asymmetry of Call and Put Prices''
4.35 Analysis of the Price Curves of a Few Other Basic Option Strategies: Simple Time Spreads
4.36 The Greeks
4.37 The Greeks for Call Options and Put Options
4.38 Graphical Illustration of the Greeks of Call Options
4.39 Graphical Illustration of the Greeks of Put Options
4.40 Delta and Gamma: Analysis of a Put Bull Spread
4.41 Test Simulations of Exit Strategies for Bull Put Spread Combinations
4.42 Delta/Gamma Hedging
4.43 Delta/Gamma Hedging: A Realistic Example
References
