Derivative Security Pricing: Techniques, Methods and Applications

✍ Scribed by Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2015
• Tongue: English
• Leaves: 616
• Series: Dynamic Modeling and Econometrics in Economics and Finance 21
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Front Matter....Pages 1-1
The Stock Option Problem....Pages 3-6
Stochastic Processes for Asset Price Modelling....Pages 7-36
An Initial Attempt at Pricing an Option....Pages 37-53
The Stochastic Differential Equation....Pages 55-91
Manipulating Stochastic Differential Equations and Stochastic Integrals....Pages 93-110
Ito’s Lemma and Its Applications....Pages 111-143
The Continuous Hedging Argument....Pages 145-156
The Martingale Approach....Pages 157-189
The Partial Differential Equation Approach Under Geometric Brownian Motion....Pages 191-206
Pricing Derivative Securities: A General Approach....Pages 207-234
Applying the General Pricing Framework....Pages 235-249
Jump-Diffusion Processes....Pages 251-271
Option Pricing Under Jump-Diffusion Processes....Pages 273-293
Partial Differential Equation Approach Under Geometric Jump-Diffusion Process....Pages 295-314
Stochastic Volatility....Pages 315-347
Pricing the American Feature....Pages 349-369
Pricing Options Using Binomial Trees....Pages 371-387
Volatility Smiles....Pages 389-401
Front Matter....Pages 403-403
Allowing for Stochastic Interest Rates in the Black–Scholes Model....Pages 405-417
Change of Numeraire....Pages 419-430
Front Matter....Pages 403-403
The Paradigm Interest Rate Option Problem....Pages 431-437
Modelling Interest Rate Dynamics....Pages 439-467
Interest Rate Derivatives: One Factor Spot Rate Models....Pages 469-504
Interest Rate Derivatives: Multi-Factor Models....Pages 505-528
The Heath–Jarrow–Morton Framework....Pages 529-568
The LIBOR Market Model....Pages 569-604
Back Matter....Pages 605-616

✦ Subjects

Finance/Investment/Banking; Quantitative Finance; Financial Economics; Probability Theory and Stochastic Processes; Optimization; Operation Research/Decision Theory