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Finance with Monte Carlo

  • Textbook
  • © 2013

Overview

Authors:
  1. Ronald W. Shonkwiler

    1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

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  • Students will learn by doing; implementing concepts of each chapter into code and experimenting with the outcome
  • Exploits the greatest virtue of the Monte Carlo method – providing results for exotic probability models
  • Students will learn a lot about options in addition to usage of mathematical models
  • Focus on Monte Carlo methods allows for students to travel a short road from theory to practical applications
  • Presents "standard" models involving Random Walks with GBM but includes other distributions as well
  • Includes supplementary material: sn.pub/extras

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Geometric Brownian Motion and the Efficient Market Hypothesis

    • Ronald W. Shonkwiler
    Pages 1-31

  3. Return and Risk

    • Ronald W. Shonkwiler
    Pages 33-75

  4. Forward and Option Contracts and Their Pricing

    • Ronald W. Shonkwiler
    Pages 77-115

  5. Pricing Exotic Options

    • Ronald W. Shonkwiler
    Pages 117-134

  6. Option Trading Strategies

    • Ronald W. Shonkwiler
    Pages 135-164

  7. Alternatives to GBM Prices

    • Ronald W. Shonkwiler
    Pages 165-189

  8. Kelly’s Criterion

    • Ronald W. Shonkwiler
    Pages 191-211

  9. Back Matter

    Pages 213-250
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Keywords

About this book

This text introduces upper division undergraduate/beginning graduate students in mathematics, finance, or economics, to the core topics of a beginning course in finance/financial engineering. Particular emphasis is placed on exploiting the power of the Monte Carlo method to illustrate and explore financial principles. Monte Carlo is the uniquely appropriate tool for modeling the random factors that drive financial markets and simulating their implications.

The Monte Carlo method is introduced early and it is used in conjunction with the geometric Brownian motion model (GBM) to illustrate and analyze the topics covered in the remainder of the text. Placing focus on Monte Carlo methods allows for students to travel a short road from theory to practical applications.

Coverage includes investment science, mean-variance portfolio theory, option pricing principles, exotic options, option trading strategies, jump diffusion and exponential Lévy alternative models, and the Kelly criterion for maximizing investment growth.

Novel features:

  • inclusion of both portfolio theory and contingent claim analysis in a single text
  • pricing methodology for exotic options
  • expectation analysis of option trading strategies
  • pricing models that transcend the Black–Scholes framework
  • optimizing investment allocations
  • concepts thoroughly explored through numerous simulation exercises
  • numerous worked examples and illustrations

The mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language.

The mathematical background required is a year and one-half course in calculus, matrix algebra covering solutions of linear systems, and a knowledge of probability including expectation, densities and the normal distribution. A refresher for these topics is presented in the Appendices. The programming background needed is how to code branching, loops and subroutines in some mathematical or general purpose language.

Also by the author: (with F. Mendivil) Explorations in Monte Carlo, ©2009, ISBN: 978-0-387-87836-2; (with J. Herod) Mathematical Biology: An Introduction with Maple and Matlab, Second edition, ©2009, ISBN: 978-0-387-70983-3.

Authors and Affiliations

  • School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Ronald W. Shonkwiler

About the author

Ronald W. Shonkwiler is a Professor Emeritus in the School of Mathematics at the Georgia Institute of Technology. He received his Masters in Mathematics in 1967, and then his PH.D. in Mathematics in 1970 from the University of Colorado, Boulder. His research includes optimization by Monte Carlo methods, computer geometry, fractal geometry, mathematical epidemiology, neural networks, and mathematical finance. Ronald W. Shonkwiler previously published two books with Springer in the UTM series. "Explorations in Monte Carlo Methods" 2009, ISBN: 978-0-387-87836-2 and "Mathematical Biology, 2nd ed" 2009, ISBN: 978-0-387-70983-3.

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