The mathematics of financial markets within everyone's reach
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The mathematics of financial markets within everyone's reach

An introduction without formulas in the main text

About the Book

The investment possibilities in the financial markets have increased dramatically in recent years. Markets that until recently were completely inaccessible to small investors are now completely open to the participation of anyone through mobile applications.

However, knowledge about the mathematical laws that govern these markets have not spread among the investment community at the same speed as the possibilities of access. One of the reasons is that practically all the texts dedicated to Mathematical Finance are of a technical nature, and show advanced mathematical content in such a rigorous way, that they are beyond the reach of the vast majority of interested people.

The main objective of this book is to fill this gap, allowing all those interested in knowing the laws that govern the financial markets, and who lack advanced mathematical knowledge, to have a first approach to the fundamental concepts without being overwhelmed by mathematical formalism. Thus, the reader will find in this book a gentle introduction to Mathematical Finance, with all the rigor, but in such a way that it can be approached without prior mathematical knowledge, beyond basic operations, some simple graphs and an intuitive knowledge of probability.

Despite all that has been said above, as a passionate for mathematical modeling, I could not exclude from reading the book all those with a more solid mathematical background and who want to introduce or delve into Mathematical Finance. For them, at the end of each chapter, I have added a section with bibliographic references that will allow those who wish to do so, to enter in depth in the study of the concepts covered. In addition, the book has an alphabetical index, included in the final part, in which all the concepts treated in it can be found, with a reference to the first page in which they appear. In this way, the book can be used as a dictionary of basic concepts.

Another important aspect of the book is the inclusion of footnotes throughout the text, in which, in addition to clarifying certain concepts, I present the mathematical formulas related to them. Those readers with a special aversion to mathematical symbols and expressions can avoid reading them without undermining the understanding of what is exposed. However, I encourage you to read them, not only because they help clarify the concepts, but also to allow yourself to discover and appreciate the elegance and beauty of the mathematics that underlie financial markets.

About the Author

Alberto Bueno Guerrrero
Alberto Bueno Guerrrero

Alberto Bueno Guerrero has a degree in Physics, a degree in Economics and a PhD in Banking and Finance. Since he got his doctorate, he has dedicated himself to research in Mathematical Finance. His work has been presented at various international conferences and published in journals such as Quantitative Finance, Journal of Derivatives and Chaos, Solitons and Fractals. He has also acted as an anonymous reviewer for various journals, and regularly reviews academic articles for Mathematical Reviews of the American Mathematical Society.

Table of Contents

  • 1. The mysterious movement of Mr. Brown
    • 1.1 A bit of history
    • 1.2 Stochastic processes
    • 1.3 Brownian motion
    • 1.4 Properties of Brownian motion
    • 1.5 Bibliography of the chapter
  • 2. Are markets efficient?
    • 2.1 Bachelier
    • 2.2 Samuelson
    • 2.3 Fama
    • 2.4 Mandelbrot
    • 2.5 Bibliography of the chapter
  • 3. Free lunches
    • 3.1 Arbitrage
    • 3.2 Options
    • 3.3 Uses of options
    • 3.4 The binomial model
    • 3.5 The equivalent martingale probability measure
    • 3.6 Properties of the measure Q
    • 3.7 The first fundamental theorem of asset pricing
    • 3.8 The second fundamental theorem of asset pricing
    • 3.9 Bibliography of the chapter
  • 4. Noisy dynamics
    • 4.1 Stochastic differential equations
    • 4.2 Linear stochastic differential equations
    • 4.3 Geometric Brownian motion
    • 4.4 The stochastic exponential
    • 4.5 Itô's rule
    • 4.6 The Girsanov theorem
    • 4.7 The martingale representation theorem
    • 4.8 Bibliography of the chapter
  • 5. Black and Scholes (and Merton)
    • 5.1 Geometric Brownian motion
    • 5.2 Properties of geometric Brownian motion
    • 5.3 Geometric Brownian motion under Q
    • 5.4 The Black-Scholes formula
    • 5.5 The Nobel prize
    • 5.6 Bibliography of the chapter
  • 6. To Black-Scholes and beyond
    • 6.1 Put-call parity
    • 6.2 The Greeks
    • 6.3 Delta hedging
    • 6.4 The implied volatility
    • 6.5 Completeness
    • 6.6 Bibliography of the chapter
  • 7. He who promises runs in debt
    • 7.1 Bonds and interest rates
    • 7.2 The duration of a bond portfolio
    • 7.3 Duration and price risk
    • 7.4 Duration and immunization
    • 7.5 Bibliography of the chapter
  • 8. Interesting rates
    • 8.1 Interest rate derivatives
    • 8.2 Affine models
    • 8.3 Heath, Jarrow and Morton
    • 8.4 Infinite-dimensional models
    • 8.5 Forward measures
    • 8.6 Derivative valuation
    • 8.7 Completeness
    • 8.8 Bibliography of the chapter
  • Bibliography
  • Index
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