Option pricing in incomplete markets : modeling based on geometric Levy 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 Levy process (GLP) is a typical e...
| Основен автор: | Miyahara, Yoshio. |
|---|---|
| Формат: | Електронна книга |
| Език: | English |
| Публикувано: |
London :
Imperial College Press,
2012.
|
| Серия: |
Series in quantitative finance ;
v. 3. |
| Предмети: | |
| Онлайн достъп: |
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=516760 |
| Подобни документи: |
Print version:Miyahara, Yoshio, 1944-:
Option pricing in incomplete markets. |
Съдържание:
- 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.