Option pricing in incomplete markets : modeling based on geometric Levy processes and minimal entropy martingale measures / Yoshio Miyahara.

Format:

Book

Author/Creator:

Miyahara, Yoshio.

Series:

Series in quantitative finance ; v. 3.

Series in quantitative finance, 1756-1604 ; v. 3

Language:

English

Subjects (All):

Options (Finance)--Prices--Mathematical models.

Options (Finance).

Pricing--Mathematical models.

Pricing.

Equilibrium (Economics)--Mathematical models.

Equilibrium (Economics).

Uncertainty--Mathematical models.

Uncertainty.

Finance--Mathematical models.

Finance.

Physical Description:

1 online resource (200 p.)

Place of Publication:

London : Imperial College Press, 2012.

Language Note:

English

Summary:

This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric Lévy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure. This volume also presents the calibration procedure of the [GLP \& MEMM] model that has been widely used in the application of practical problems.

Contents:

Preface; Contents; 1. Basic Concepts in Mathematical Finance; 1.1 Price Processes; 1.2 No-arbitrage and Martingale Measures; 1.3 Complete and Incomplete Markets; 1.4 Fundamental Theorems; 1.5 The Black-Scholes Model; 1.6 Properties of the Black-Scholes Model; 1.6.1 Distribution of log returns; 1.6.2 Historical volatility and implied volatility; 1.7 Generalization of the Black-Scholes Model; 1.7.1 Geometric Levy process models; 1.7.2 Stochastic volatility models; Notes; 2. Levy Processes and Geometric Levy Process Models; 2.1 Levy Processes; 2.1.1 Definitions and properties

2.1.2 Infinitely divisible distributions2.1.3 Canonical representation of Levy processes; 2.2 Geometric Levy Process Models; 2.2.1 The geometric Brownian motion model; 2.2.2 Geometric compound Poisson models; 2.2.3 Jump-diffusion models; 2.2.4 Geometric variance gamma models; 2.2.5 Geometric stable process models; 2.2.6 Geometric CGMY models; 2.3 Doleans-Dade Exponential; Notes; 3. Equivalent Martingale Measures; 3.1 Equivalent Martingale Measure Methods; 3.2 Equivalent Martingale Measures for Geometric Levy Processes; 3.2.1 Candidates for suitable equivalent martingale measure

3.3 Methods for Construction of Martingale Measures3.3.1 Variance optimal martingale measure (VOMM); 3.3.2 Minimal entropy martingale measure (MEMM); Notes; 4. Esscher-Transformed Martingale Measures; 4.1 Esscher Transformation; 4.2 Esscher-Transformed Martingale Measure for Geometric Levy Processes; 4.2.1 Simple-return process and compound-return process; 4.2.2 Two kinds of Esscher-transformed martingale measure; 4.3 Existence Theorems of P(ESSMM) and P(ESSMM) for Geometric Levy Processes; 4.3.1 Existence theorem of P(ESSMM); 4.3.2 Existence theorem of P(ESSMM)

4.4 Comparison of P(ESSMM) and P(ESSMM)4.5 Other Examples of Esscher-Transformed Martingale Measures; Notes; 5. Minimax Martingale Measures and Minimal Distance Martingale Measures; 5.1 Utility Function, Duality, and Minimax Martingale Measures; 5.2 Distance Function Corresponding to Utility Function; 5.3 Minimal Distance Martingale Measures; Notes; 6. Minimal Distance Martingale Measures for Geometric Levy Processes; 6.1 Minimal Distance Problem; 6.2 The Minimal Variance Equivalent Martingale Measure (MVEMM); 6.2.1 Deterministic problem; 6.2.2 Existence theorem of the MVEMM

6.2.3 Generating triplet of Zt under MVEMM6.3 The Minimal Lq Equivalent Martingale Measure; 6.3.1 The case of q > 1; 6.3.2 The case of 0 < q < 1; 6.3.3 The case of q < 0; 6.4 Minimal Entropy Martingale Measures; 6.5 Convergence of MLqEMM to MEMM (as q # 1); Notes; 7. The [GLP & MEMM] Pricing Model; 7.1 The Model; 7.1.1 Sufficient condition for the existence of MEMM; 7.1.2 Properties of geometric Levy processes under MEMM; 7.2 Examples of [GLP & MEMM] Pricing Model; 7.2.1 Geometric (Brownian motion + compound Poisson) model (or jump-diffusion model) ([GJD & MEMM])

7.2.2 Geometric variance gamma model ([GVG & MEMM])

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-84816-348-7

OCLC:

858228200