2012 Fiscal Year Final Research Report
Research for fractal market influenced by stochastic volatility
| Project/Area Number |
22510161
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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 |
Social systems engineering/Safety system
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| Research Institution | Kanagawa University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SHINDO Susumu 神奈川大学, 工学部, 教授 (60322533)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 確率ボラティリティ / フラクショナルブラウン運動 / ハースト指数 / 確率微分方程式 / ブラック‐ショールズ方程式 / ヨーロッパ型コールオプション / オルンシュタイン‐ウーレンベック過程 / 特異摂動 |
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| Research Abstract |
In the financial model derived by Black, F. and Scholes, M. (1973), the volatility, which represents the degree of randomness of the asset price, is quantified by a constant parameter. In this research, to obtain a more realistic model, the volatilities are formulated by fractional stochastic processes which have statistic self-similarity and dependence on the memory to the past. Moreover, in the case when the volatility-driving processes have the ‘long and short term-memories’ and the ‘fast and slow mean-reversions’, we solved the problem for option pricing in financial derivatives.
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Research Products
(39 results)
