6

251-286

36

 

John Wiley & Sons, Inc. (Visit publisher website)

2005

English

 

 

 

Intermediate

 

 

Quantitative analysis, continuous-time models, call/put options, continuous-time stochastic process, Wiener process, standard brownian motion, Donsker`s theorem, generalized Wiener process, Ito process, Ito’s lemma, differentiation, stochastic differentiation, estimation of μ and σ , stock price distributions, log returns, Black–Scholes differential equation, Black–Scholes pricing formulas, risk-neutrality, lower bounds of European options, marginal effects of Black-Scholes variables, Ito`s lemma for several stochastic processes, stochastic integral, jump diffusion models, option pricing under jump diffusion, estimation of continuous-time models

 

This chapter provides an overview of the properties of continuous time stochastic processes built from the Wiener increments and their application as models for the price of the underlying asset in derivative valuation. Kou (2002) option pricing model for an underlying price characterized by a jump diffusion process is developed. References to the existing literature on methods of estimation for stochastic processes are provided.

 

6.1 Options
6.2 Some Continuous-Time Stochastic Processes
6.2.1 The Wiener Process
6.2.2 Generalized Wiener Processes
6.2.3 Ito Processes
6.3 Ito’s Lemma
6.3.1 Review of Differentiation
6.3.2 Stochastic Differentiation
6.3.3 An Application
6.3.4 Estimation of μ and σ
6.4 Distributions of Stock Prices and Log Returns
6.5 Derivation of Black–Scholes Differential Equation
6.6 Black–Scholes Pricing Formulas
6.6.1 Risk-Neutral World
6.6.2 Formulas
6.6.3 Lower Bounds of European Options
6.6.4 Discussion
6.7 An Extension of Ito’s Lemma
6.8 Stochastic Integral
6.9 Jump Diffusion Models
6.9.1 Option Pricing Under Jump Diffusion
6.10 Estimation of Continuous-Time Models
Appendix A: Integration of Black–Scholes Formula
Appendix B: Approximation to Standard Normal
Probability
Exercises
References

 

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The Second Edition of this critically acclaimed text provides a comprehensive and systematic introduction to financial econometric models and their applications in modeling and predicting financial time series data. This edition continues to emphasize empirical financial data and focuses on real-world examples. Following this approach, readers will master key aspects of financial time series, including volatility modeling, neural network applications, market microstructure and high-frequency financial data, continuous-time models and Ito`s Lemma, Value at Risk, multiple returns analysis, financial factor models, and econometric modeling via computation-intensive methods.

The author begins with the basic characteristics of financial time series data, setting the foundation for the three main topics:

* Analysis and application of univariate financial time series
* Return series of multiple assets
* Bayesian inference in finance methods

This new edition is a thoroughly revised and updated text, including the addition of S-Plus® commands and illustrations. Among the new material, readers will find:

* Consistent covariance estimation under heteroscedasticity and serial correlation
* Alternative approaches to volatility modeling
* Financial factor models
* State-space models
* Kalman filtering
* Estimation of stochastic diffusion models

This is an ideal textbook for MBA students as well as a reference for researchers and professionals in business and finance.