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

Published London : Imperial College Press, 2012

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Description 1 online resource (xiv, 185 pages) Series Series in quantitative finance, 1756-1604 ; v. 3 Series in quantitative finance ; v. 3. 1756-1604 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. 1.7. Generalization of the Black-Scholes model -- 2. Levy processes and geometric Levy process models. 2.1. Levy processes. 2.2. Geometric Levy process models. 2.3. Doleans-Dade exponential -- 3. Equivalent Martingale measures. 3.1. Equivalent Martingale measure methods. 3.2. Equivalent Martingale measures for geometric Levy processes. 3.3. Methods for construction of Martingale measures -- 4. Esscher-transformed Martingale measures. 4.1. Esscher transformation. 4.2. Esscher-transformed Martingale measure for geometric Levy processes. 4.3. Existence theorems of P(ESSMM) and P[symbol](ESSMM) for geometric Levy processes. 4.4. Comparison of P(ESSMM) and P[symbol](ESSMM). 4.5. Other examples of Esscher-transformed Martingale measures 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 -- 6. Minimal distance Martingale measures for geometric Levy processes. 6.1. Minimal distance problem. 6.2. The Minimal Variance Equivalent Martingale Measure (MVEMM). 6.3. The Minimal L[symbol] equivalent Martingale measure. 6.4. Minimal entropy Martingale measures. 6.5. Convergence of ML[symbol]EMM to MEMM (as q [symbol] 1) -- 7. The [GLP & MEMM] pricing model. 7.1. The model. 7.2. Examples of [GLP & MEMM] pricing model. 7.3. Why the geometric Levy process? 7.4. Why the MEMM? 7.5. Comparison of equivalent Martingale measures for geometric Levy processes. 7.6. The explicit form of Levy measure of Z[symbol] under an equivalent Martingale measure 8. Calibration and fitness analysis of the [GLP & MEMM] mode. 8.1. The physical world and the MEMM world. 8.2. Reproducibility of volatility smile/smirk property of the [GLP & MEMM] model. 8.3. Calibration of [GLP & MEMM] pricing model. 8.4. Fitness analysis -- 9. The [GSP & MEMM] pricing model. 9.1. The physical world and the MEMM world. 9.2. Calibration by the [GSP & MEMM] pricing model. 9.3. Application of the calibrated process to dollar-yen currency options -- 10. The multi-dimensional [GLP & MEMM] pricing model. 10.1. Multi-dimensional Levy processes. 10.2. Multi-dimensional geometric Levy processes. 10.3. Esscher MM and MEMM. 10.4. Application to portfolio evaluation. 10.5. Risk-sensitive evaluation of growth rate 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 Levy 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 Bibliography Includes bibliographical references and index Subject Equilibrium (Economics) -- Mathematical models. Finance -- Mathematical models. Options (Finance) -- Prices -- Mathematical models. Pricing -- Mathematical models. Uncertainty -- Mathematical models. Form Electronic book ISBN 1299672191 (ebk) 1848163487 (electronic bk.) 9781299672192 (ebk) 9781848163485 (electronic bk.)

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