2011 Fiscal Year Final Research Report
A Study of Mathematical Models for Risk Measurement
| Project/Area Number |
21500282
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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 |
Statistical science
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| Research Institution | Seijo University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 定量的リスク管理 / 計量ファイナンス |
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| Research Abstract |
We take the class of distortion risk measures as the object of our study because it satisfies many desirable properties as a measure of financial risk. We first consider estimation problem ; when data can be considered as realizations of weakly dependent stationary time series, we show that our estimator, which is of the L-statistics form, has strong consistency and asymptotic normality. We also propose an estimator for the asymptotic variance using spectral analysis, and investigate a bootstrap procedure for bias correction including its validity. Using Monte Carlo simulation, we examine the performance of the estimator, comparing with some distortion risk measures and the value-at-risk(VaR). Furthermore, we propose some backtesting methods with distortion risk measures and compute risk allocation contributions. We then perform a comparative analysis of distortion risk measures under various distributional scenarios.
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