Binomial Models in Finance

1. Front Matter

   Pages I-XIII

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2. Introduction

   Pages 1-11

3. The Binomial Model for Stock Options

   Pages 13-39

4. The Binomial Model for Other Contracts

   Pages 41-64

5. Multiperiod Binomial Models

   Pages 65-80

6. Hedging

   Pages 81-88

7. Forward and Futures Contracts

   Pages 89-96

8. American and Exotic Option Pricing

   Pages 97-107

9. Path-Dependent Options

   Pages 109-119

10. The Greeks

    Pages 121-126

11. Dividends

    Pages 127-134

12. Implied Volatility Trees

    Pages 135-151

13. Implied Binomial Trees

    Pages 153-170

14. Interest Rate Models

    Pages 171-208

15. Real Options

    Pages 209-236

16. The Binomial Distribution

    Pages 237-248

17. An Application of Linear Programming

    Pages 249-267

18. Volatility Estimation

    Pages 269-278

19. Existence of a Solution

    Pages 279-283

20. Some Generalizations

    Pages 285-288

This book describes the modelling of prices of ?nancial assets in a simple d- crete time, discrete state, binomial framework. By avoiding the mathematical technicalitiesofcontinuoustime?nancewehopewehavemadethematerial accessible to a wide audience. Some of the developments and formulae appear here for the ?rst time in book form. We hope our book will appeal to various audiences. These include MBA s- dents,upperlevelundergraduatestudents,beginningdoctoralstudents,qu- titative analysts at a basic level and senior executives who seek material on new developments in ?nance at an accessible level. The basic building block in our book is the one-step binomial model where a known price today can take one of two possible values at a future time, which might, for example, be tomorrow, or next month, or next year. In this simple situation “risk neutral pricing” can be de?ned and the model can be applied to price forward contracts, exchange rate contracts and interest rate derivatives. In a few places we discuss multinomial models to explain the notions of incomplete markets and how pricing can be viewed in such a context, where unique prices are no longer available. The simple one-period framework can then be extended to multi-period m- els.TheCox-Ross-RubinsteinapproximationtotheBlackScholesoptionpr- ing formula is an immediate consequence. American, barrier and exotic - tions can all be discussed and priced using binomial models. More precise modelling issues such as implied volatility trees and implied binomial trees are treated, as well as interest rate models like those due to Ho and Lee; and Black, Derman and Toy.

• Futures
• Option Pricing
• Options
• STATISTICA
• Volatility
• derivatives
• hedging
• linear optimization
• mathematics
• programming
• spreadsheet
• quantitative finance

From the reviews:

"Overall, this is an excellent 'workbook' for practitioners who seek to understand and apply financial asset price models by working through a comprehensive collection of both theoretical and dataset-driven numerical examples, follwoed by up to 15 end-of-chapter exercises with elaborated parts taht help clarify the mathematical and computational aspects of the chapter." Wai F. Chiu for the Journal of the American Statistical Association, December 2006

"This is a textbook on the mathematics of pricing and hedging financial derivatives with discrete stochastic models. It is directed towards a readership that is interested in the principles and applications of mathematical finance … . A nice feature is the very clear descriptions of financial terms, which, on the one hand, are often missing in more mathematics-oriented books and, on the other hand, can be somewhat imprecise in textbooks aiming at the business community." (A. Schied, Short Book Reviews, Vol. 26 (2), 2006)

"The book is written by leading specialists in modern stochastic financial modeling. … The book is well written, with a good balance between mathematical tools and arguments and financial topics. It is nice to see proofs of several important properties of financial characteristics and rules for option pricing. Specific numerical examples are given to illustrate ideas and rules. … Without any reservations the book can be strongly recommended not only to institutional libraries but also to anybody working or with interests in stochastic financial modeling." (Jordan M. Stoyanov, Zentralblatt MATH, Vol. 1107 (9), 2007)

• Discipline of Applied Mathematics, University of Adelaide, Adelaide, Australia

  John Hoek

• Haskayne School of Business Scurfield Hall, University of Calgary, Calgary, Canada

  Robert J. Elliott

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