1. Geometric Brownian Motion and the Efficient Market Hypothesis.- 2. Return and Risk.- 3. Forward and Option Contracts and their Pricing.- 4. Pricing Exotic Options.- 5. Option Trading Strategies.- 6. Alternative to GBM Prices.- _7. Kelly's Criterion.- Appendices.- A. Some Mathematical Background Topics.- B. Stochastic Calculus.- C. Convergence of the Binomial Method.- D. Variance Reduction Techniques.- E. Shell Sort.- F. Next Day Prices Program.- References.- List of Notation.- List of Algorithms.- Index.
Über den Autor
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.
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
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