Option Pricing in Incomplete Markets

Modeling Based on Geometric Lévy Processes and Minimal Entropy Martingale Measures

Nonfiction, Science & Nature, Mathematics, Applied, Business & Finance, Finance & Investing, Finance

• Author: Yoshio Miyahara
• ISBN: 9781848169180
• Publisher: World Scientific Publishing Company
• Publication: November 22, 2011
• Imprint: ICP
• Language: English

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:

• Basic Concepts in Mathematical Finance
• Lévy Processes and Geometric Lévy Process Models
• Equivalent Martingale Measures
• Esscher Transformed Martingale Measures
• Minimax Martingale Measures and Minimal Distance Martingale Measures
• Minimal Distance Martingale Measures for Geometric Lévy Processes
• The [GLP & MEMM] Pricing Model
• Calibration and Fitness Analysis of the [GLP & MEMM] Model
• The [GSP & MEMM] Pricing Model
• The Multi-Dimensional [GLP & MEMM] Pricing Model

Readership: Academics, graduate students and practitioners in mathematical finance.
Key Features:

• Provides high treatment on wide classes of jump processes with fat tails, and typically stable processes
• Contains a unique and unifying method, namely the minimal entropy martingale measure
• Well-furnished with the procedure for the applications and calibrations to practical problems