Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Introduction and Basic Concepts
- Part II Firm Valuation and Capital Structure
- Part III Fixed Income Securities and Options
- 7 Valuation of Bonds and Interest Rates
- 8 Markets for Options
- 9 Arbitrage and Binomial Model
- 10 Brownian Motion and Itō's Lemma
- 11 The Black–Scholes–Merton Model
- 12 Exotic Options
- 13 Risk-Neutral Valuation and Martingales
- Part IV Portfolio Management Theory
- Bibliography
- Index
9 - Arbitrage and Binomial Model
from Part III - Fixed Income Securities and Options
Published online by Cambridge University Press: 05 July 2013
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Introduction and Basic Concepts
- Part II Firm Valuation and Capital Structure
- Part III Fixed Income Securities and Options
- 7 Valuation of Bonds and Interest Rates
- 8 Markets for Options
- 9 Arbitrage and Binomial Model
- 10 Brownian Motion and Itō's Lemma
- 11 The Black–Scholes–Merton Model
- 12 Exotic Options
- 13 Risk-Neutral Valuation and Martingales
- Part IV Portfolio Management Theory
- Bibliography
- Index
Summary
INTRODUCTION
An arbitrage opportunity refers to the possibility of deriving instantaneous profit without any risk. For instance, suppose gold is being sold at 400 dollars per ounce in city I but 399.90 dollars in a different city II. Then a trader can buy gold from city II and sell it in city I to make a riskless profit of 10 cents per ounce. This is arbitrage. That is, an arbitrage opportunity represents the production of something out of nothing. The non-arbitrage principle means the rule of a single price. The key principle behind the idea of asset pricing in financial economics is the principle of non-arbitrage. In fact, even if there are scopes for arbitrage opportunities, price adjustment will eliminate them eventually. Essential to the non-existence of arbitrage opportunities in our set up is risk-neutral valuation. According to risk-neutral valuation, the current price of a financial asset equals the expected future price of the asset discounted at the risk-free rate of interest. The central idea underlying risk-neutral valuation parallels the idea implicit in the certainty equivalent. In the certainty equivalent method a risky variable is replaced by one that can be obtained with certainty. The time periods considered in the framework for risk-neutral valuation are discrete.
- Type
- Chapter
- Information
- An Outline of Financial Economics , pp. 134 - 153Publisher: Anthem PressPrint publication year: 2013