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Über dieses Buch

The book presents applications of stochastic calculus to derivative security pricing and interest rate modelling. By focusing more on the financial intuition of the applications rather than the mathematical formalities, the book provides the essential knowledge and understanding of fundamental concepts of stochastic finance, and how to implement them to develop pricing models for derivatives as well as to model spot and forward interest rates. Furthermore an extensive overview of the associated literature is presented and its relevance and applicability are discussed. Most of the key concepts are covered including Ito’s Lemma, martingales, Girsanov’s theorem, Brownian motion, jump processes, stochastic volatility, American feature and binomial trees. The book is beneficial to higher-degree research students, academics and practitioners as it provides the elementary theoretical tools to apply the techniques of stochastic finance in research or industrial problems in the field.

Inhaltsverzeichnis

Frontmatter

The Fundamentals of Derivative Security Pricing

Frontmatter

2015 | OriginalPaper | Buchkapitel

Chapter 1. The Stock Option Problem

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 2. Stochastic Processes for Asset Price Modelling

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 3. An Initial Attempt at Pricing an Option

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 4. The Stochastic Differential Equation

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 5. Manipulating Stochastic Differential Equations and Stochastic Integrals

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 6. Ito’s Lemma and Its Applications

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 7. The Continuous Hedging Argument

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 8. The Martingale Approach

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 9. The Partial Differential Equation Approach Under Geometric Brownian Motion

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 10. Pricing Derivative Securities: A General Approach

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 11. Applying the General Pricing Framework

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 12. Jump-Diffusion Processes

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 13. Option Pricing Under Jump-Diffusion Processes

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 14. Partial Differential Equation Approach Under Geometric Jump-Diffusion Process

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 15. Stochastic Volatility

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 16. Pricing the American Feature

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 17. Pricing Options Using Binomial Trees

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 18. Volatility Smiles

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

Interest Rate Modelling

Frontmatter

2015 | OriginalPaper | Buchkapitel

Chapter 19. Allowing for Stochastic Interest Rates in the Black–Scholes Model

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 20. Change of Numeraire

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 21. The Paradigm Interest Rate Option Problem

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 22. Modelling Interest Rate Dynamics

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 23. Interest Rate Derivatives: One Factor Spot Rate Models

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 24. Interest Rate Derivatives: Multi-Factor Models

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 25. The Heath–Jarrow–Morton Framework

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

2015 | OriginalPaper | Buchkapitel

Chapter 26. The LIBOR Market Model

Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos

Backmatter

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