American-type options : stochastic approximation methods. Volume 1 / Dmitrii S. Silvestrov.

Format:

Book

Author/Creator:

Silʹvestrov, D. S. (Dmitriĭ Sergeevich)

Series:

De Gruyter studies in mathematics ; 56.

De Gruyter studies in mathematics, 0179-0986 ; volume 56

Language:

English

Subjects (All):

Options (Finance)--Mathematical models.

Options (Finance).

Stochastic approximation.

Markov processes.

Business mathematics.

Physical Description:

1 online resource (520 p.)

Edition:

1st ed.

Place of Publication:

Berlin : De Gruyter, [2014]

Language Note:

English

Summary:

The book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area. This book is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.

Contents:

Front matter

Preface

Contents

1. Multivariate modulated Markov log-price processes (LPP)

2. American-type options

3. Backward recurrence reward algorithms

4. Upper bounds for option rewards

5. Convergence of option rewards - I

6. Convergence of option rewards - II

7. Space-skeleton reward approximations

8. Convergence of rewards for Markov Gaussian LPP

9. Tree-type approximations for Markov Gaussian LPP

10. Convergence of tree-type reward approximations

Bibliographical Remarks

Bibliography

Index

Back matter

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed January 7, 2014).

ISBN:

3-11-032982-4

OCLC:

865333012