Analytically tractable stochastic stock price models

Media type: E-Book

Title: Analytically tractable stochastic stock price models

Contributor: Gulisashvili, Archil [Author]

imprint: Berlin; Heidelberg [u.a.]t: Springer, 2012
Online-Ausg., [S.l.]: eblib, 2012

Language: English

ISBN: 9783642312137

RVK notation: QH 237 : Zeitreihenanalyse. Anwendungen stochastischer Prozesse, stochastische Prozesse, stochastische Differentialgleichungen

Keywords: Aktienkurs > Optionspreis > Volatilität > Dichte > Stochastisches Modell

Type of reproduction: Online-Ausg.

Place of reproduction: [S.l.]: eblib, 2012

Origination:

Footnote: Description based upon print version of record

Description: Analytically Tractable Stochastic Stock Price Models; Preface; Acknowledgements; Contents; Chapter 1: Volatility Processes; 1.1 Brownian Motion; 1.2 Geometric Brownian Motion; 1.3 Long-Time Behavior of Marginal Distributions; 1.4 Ornstein-Uhlenbeck Processes; 1.5 Ornstein-Uhlenbeck Processes and Time-Changed Brownian Motions; 1.6 Absolute Value of an Ornstein-Uhlenbeck Process; 1.7 Squared Bessel Processes and CIR Processes; 1.8 Squared Bessel Processes and Sums of the Squares of Independent Brownian Motions; 1.9 Chi-Square Distributions; 1.10 Noncentral Chi-Square Distributions

1.11 Marginal Distributions of Squared Bessel Processes. Formulations1.12 Laplace Transforms of Marginal Distributions; 1.13 Marginal Distributions of Squared Bessel Processes. Proofs; 1.14 Time-Changed Squared Bessel Processes and CIR Processes; 1.15 Marginal Distributions of CIR Processes; 1.16 Ornstein-Uhlenbeck Processes and CIR Processes; 1.17 Notes and References; Chapter 2: Stock Price Models with Stochastic Volatility; 2.1 Stochastic Volatility; 2.2 Correlated Stochastic Volatility Models; 2.3 Hull-White, Stein-Stein, and Heston Models

2.4 Relations Between Stock Price Densities in Stein-Stein and Heston Models2.5 Girsanov's Theorem; 2.6 Risk-Neutral Measures; 2.7 Risk-Neutral Measures for Uncorrelated Hull-White Models; 2.8 Local Times for Semimartingales; 2.9 Risk-Neutral Measures for Uncorrelated Stein-Stein Models; 2.10 Risk-Neutral Measures for Uncorrelated Heston Models; 2.11 Hull-White Models. Complications with Correlations; 2.12 Heston Models and Stein-Stein Models. No Complications with Correlations; 2.13 Notes and References; Chapter 3: Realized Volatility and Mixing Distributions

3.1 Asymptotic Relations Between Functions3.2 Mixing Distributions and Stock Price Distributions; 3.3 Stock Price Densities in Uncorrelated Models as Mixtures of Black-Scholes Densities; 3.4 Mixing Distributions and Heston Models; 3.5 Mixing Distributions and Hull-White Models with Driftless Volatility; 3.6 Mixing Distributions and Hull-White Models; 3.7 Mixing Distributions and Stein-Stein Models; 3.8 Notes and References; Chapter 4: Integral Transforms of Distribution Densities; 4.1 Geometric Brownian Motions and Laplace Transforms of Mixing Distributions; 4.2 Bougerol's Identity in Law

4.3 Squared Bessel Processes and Laplace Transforms of Mixing Distributions4.4 CIR Processes and Laplace Transforms of Mixing Distributions; 4.5 Ornstein-Uhlenbeck Processes and Laplace Transforms of Mixing Distributions; 4.6 Hull-White Models with Driftless Volatility and Hartman-Watson Distributions; 4.7 Mixing Density and Stock Price Density in the Correlated Hull-White Model; 4.8 Mellin Transform of the Stock Price Density in the Correlated Heston Model; 4.9 Mellin Transform of the Stock Price Density in the Correlated Stein-Stein Model; 4.10 Notes and References

Chapter 5: Asymptotic Analysis of Mixing Distributions

Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the He

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