2006 Fiscal Year Final Research Report Summary
Option Pricing Models Based on Levy Process and Entropy, and Applications
| Project/Area Number |
16540113
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya City University |
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Principal Investigator |
MIYAHARA Yoshio Nagoya City University, Graduate School of Economics, Professor, 大学院経済学研究科, 教授 (20106256)
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| Co-Investigator(Kenkyū-buntansha) |
MISAWA Tetsuya Nagoya City University, Graduate School of Economics, Professor, 大学院経済学研究科, 教授 (10190620)
IBARAKI Satoru Nagoya City University, Graduate School of Economics, Associate Professor, 大学院経済学研究科, 助教授 (10252488)
FUJIWARA Tsukasa Hyogo University of Teacher Education, Department of Mathematics, Associate Professor, 学校教育学部, 助教授 (30199385)
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| Project Period (FY) |
2004 – 2006
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| Keywords | mathematical finance / option pricing / incomplete market / geometric Levy process / equivalent martingale measure / relative entropy / calibration / geometric stable process |
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| Research Abstract |
We have studied the option pricing problems in the incomplete asset market. In the previous research we have constructed the basic frameworks of the [GLP ＆ MEMM] pricing models, in which the geometric Levy processes are adopted as the underlying asset price processes and the MEMM (=minimal entropy martingale measure) is adopted as the equivalent martingale measure. So in this research we have investigated the fundamental properties of this model and have established the method how to apply this model to the practical option pricing problems.
After that we have investigated the properties of this model by the computer simulation methods, and we have obtained a good result that this model has the possibility to realize the volatility smile/skew properties of the option prices in the markets.
Next we have made empirical analysis on the market prices of the options, and we have obtained such a result that this model fits very well to the option prices in the market in the case that the underlying asset process moves very rapidly. Especially we could have seen that the [Geometric Stable Process ＆ MEMM] model is very desirable in the sense that this model has the possibility to fit to very wide class of the option price data in the market.
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