Non-Gaussian Merton-Black-Scholes theory / Svetlana I. Boyarchenko, Sergei Z. Levendorskii.

Format:

Book

Author/Creator:

Boyarchenko, Svetlana I.

Contributor:

Levendorskiĭ, Serge, 1951-

Series:

Advanced series on statistical science & applied probability ; v. 9.

Advanced series on statistical science & applied probability ; v. 9

Language:

English

Subjects (All):

Finance--Mathematical models.

Finance.

Physical Description:

1 online resource (421 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, 2002.

Language Note:

English

Summary:

This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory. The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferentia

Contents:

Contents ; Preface ; 0.0.1 General notation ; Chapter 1 Introduction ; 1.1 The Gaussian Merton-Black-Scholes theory ; 1.2 Regular Levy Processes of Exponential type ; 1.3 Pricing of contingent claims ; 1.4 The Generalized Black-Scholes equation

1.5 Analytical methods used in the book 1.6 An overview of the results covered in the book ; 1.7 Commentary ; Chapter 2 Levy processes ; 2.1 Basic notation and definitions ; 2.2 Levy processes: general definitions ; 2.3 Levy processes as Markov processes

2.4 Boundary value problems for the Black-Scholes-type equation 2.5 Commentary ; Chapter 3 Regular Levy Processes of Exponential type in 1D ; 3.1 Model Classes ; 3.2 Two definitions of Regular Levy Processes of Exponential type

3.3 Properties of the characteristic exponents and probability densities of RLPE 3.4 Properties of the infinitesimal generators ; 3.5 A ""naive approach"" to the construction of RLPE or why they are natural from the point of view of the theory of PDO ; 3.6 The Wiener-Hopf factorization

Chapter 4 Pricing and hedging of contingent claims of European type 4.1 Equivalent Martingale Measures in a Levy market ; 4.2 Pricing of European options and the generalized Black-Scholes formula

4.3 Generalized Black-Scholes equation and its properties for different RLPE and different choices of EMM and implications for parameter fitting

Notes:

Description based upon print version of record.

Invcludes bibliographical references (p. 385-392) and index.

ISBN:

9789812777485

9812777482

OCLC:

879023457