Book contents
- Frontmatter
- Contents
- Foreword
- Preface
- 1 Probability theory: basic notions
- 2 Maximum and addition of random variables
- 3 Continuous time limit, Ito calculus and path integrals
- 4 Analysis of empirical data
- 5 Financial products and financial markets
- 6 Statistics of real prices: basic results
- 7 Non-linear correlations and volatility fluctuations
- 8 Skewness and price-volatility correlations
- 9 Cross-correlations
- 10 Risk measures
- 11 Extreme correlations and variety
- 12 Optimal portfolios
- 13 Futures and options: fundamental concepts
- 14 Options: hedging and residual risk
- 15 Options: the role of drift and correlations
- 16 Options: the Black and Scholes model
- 17 Options: some more specific problems
- 18 Options: minimum variance Monte–Carlo
- 19 The yield curve
- 20 Simple mechanisms for anomalous price statistics
- Index of most important symbols
- Index
13 - Futures and options: fundamental concepts
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Foreword
- Preface
- 1 Probability theory: basic notions
- 2 Maximum and addition of random variables
- 3 Continuous time limit, Ito calculus and path integrals
- 4 Analysis of empirical data
- 5 Financial products and financial markets
- 6 Statistics of real prices: basic results
- 7 Non-linear correlations and volatility fluctuations
- 8 Skewness and price-volatility correlations
- 9 Cross-correlations
- 10 Risk measures
- 11 Extreme correlations and variety
- 12 Optimal portfolios
- 13 Futures and options: fundamental concepts
- 14 Options: hedging and residual risk
- 15 Options: the role of drift and correlations
- 16 Options: the Black and Scholes model
- 17 Options: some more specific problems
- 18 Options: minimum variance Monte–Carlo
- 19 The yield curve
- 20 Simple mechanisms for anomalous price statistics
- Index of most important symbols
- Index
Summary
Les personnes non averties sont sujettes à se laisser induire en erreur.
(Lord Raglan, ‘Le tabou de l'inceste’, quoted by Boris Vian in L'automne à Pékin.)Introduction
Aim of the chapter
The aim of this chapter is to introduce the general theory of derivative pricing in a simple and intuitive, but rather unconventional, way. The usual presentation, which can be found in all the available books on the subject, relies on particular models where it is possible to construct riskless hedging strategies, which replicate exactly the corresponding derivative product. Since the risk is strictly zero, there is no ambiguity in the price of the derivative: it is equal to the cost of the hedging strategy. In the general case, however, these ‘perfect’ strategies do not exist. Not surprisingly for the layman, zero risk is the exception rather than the rule. Correspondingly, a suitable theory must include risk as an essential feature, which one would like to minimize. The following chapters thus aim at developing simple methods to obtain optimal strategies, residual risks, and prices of derivative products, which take into account in an adequate way the peculiar statistical nature of financial markets, that have been described in Chapters 6, 7, 8.
Strategies in uncertain conditions
A derivative product is an asset the value of which depends on the price history of another asset, the ‘underlying’. The best known examples, on which the following chapters will focus in detail, are futures and options.
- Type
- Chapter
- Information
- Theory of Financial Risk and Derivative PricingFrom Statistical Physics to Risk Management, pp. 226 - 253Publisher: Cambridge University PressPrint publication year: 2003