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Evaluating the hedging error in price processes with jumps present
Jing B.Y.1; Kong X.B.2; Liu Z.3; Zhang B.4
Source PublicationStatistics and its Interface
ISSN19387989 19387997

In this draft, we consider a hedging strategy concerning only the continuous parts of two asset price processes which have jumps. Two consistent estimators of the hedging strategy, ρ̂ and ρ̃, are presented in terms of realized bipower variation and threshold quadratic variation, respectively. Based on ρ̂, estimators for operational risk, market risk (risk due to jumps) and total risk are investigated. It turns out that the variance of ρ̂ enters into the bias of the operational risk estimator, whereas the variance is mainly due to jump influenced bipower estimation error. The convergence rate of the operational risk estimator (properly centralized) is O ((δt)̄. The convergence rate of the market risk is however O ((δt)̄. Based on ρ̃, the total risk is also studied, and it has the same convergence rate as that based on ρ̂. Besides the interest in financial econometrics, it is also of significance in a statistical sense when we are interested in estimating the quadratic variation of the corresponding unhedgeable residual process.

KeywordHedging Strategy Jump Diffusion Quadratic Variation Realized Bipower Variation Thresholdvariation Variation Of Time Volatility
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Indexed BySCI
WOS Research AreaMathematical & Computational Biology ; Mathematics
WOS SubjectMathematical & Computational Biology ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000330487100001
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Document TypeJournal article
Affiliation1.Hong Kong University of Science and Technology
2.Fudan University
3.Universidade de Macau
4.Renmin University of China
Recommended Citation
GB/T 7714
Jing B.Y.,Kong X.B.,Liu Z.,et al. Evaluating the hedging error in price processes with jumps present[J]. Statistics and its Interface,2013,6(4):413-425.
APA Jing B.Y.,Kong X.B.,Liu Z.,&Zhang B..(2013).Evaluating the hedging error in price processes with jumps present.Statistics and its Interface,6(4),413-425.
MLA Jing B.Y.,et al."Evaluating the hedging error in price processes with jumps present".Statistics and its Interface 6.4(2013):413-425.
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