Option Pricing in Incomplete Markets

Modeling Based on Geometric Lévy Processes and Minimal Entropy Martingale Measures

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