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Evaluating the hedging error in price processes with jumps present
Jing,Bing Yi1; Kong,Xin Bing2; Liu,Zhi3; Zhang,Bo4
2013
Source PublicationStatistics and its Interface
ISSN1938-7989
Volume6Issue:4Pages:413-425
Abstract

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
DOI10.4310/SII.2013.v6.n4.a1
URLView the original
Language英語English
WOS IDWOS:000330487100001
Scopus ID2-s2.0-84893426245
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Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Department of Mathematics,Hong Kong Univ. of Science and Technology,Clear Water Bay,Kowloon,Hong Kong
2.Department of Statistics,School of Management,Fudan University,Guoshun Road,Shanghai,China
3.Department of Mathematics,Faculty of Science and Technology,University of Macau,Macao
4.School of Statistics,Renmin University of China,#59 Zhongguancun Street,Beijing 100872,China
Recommended Citation
GB/T 7714
Jing,Bing Yi,Kong,Xin Bing,Liu,Zhi,et al. Evaluating the hedging error in price processes with jumps present[J]. Statistics and its Interface, 2013, 6(4), 413-425.
APA Jing,Bing Yi., Kong,Xin Bing., Liu,Zhi., & Zhang,Bo (2013). Evaluating the hedging error in price processes with jumps present. Statistics and its Interface, 6(4), 413-425.
MLA Jing,Bing Yi,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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