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, $hat{ho}$ and $ilde{ho}$, are presented in terms of realized bipower variation and threshold quadratic variation, respectively. Based on $hat{ho}$, estimators for operational risk, market risk (risk due to jumps) and total risk are investigated. It turns out that the variance of $hat{ho}$ 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 $O_P((overline{Delta t})^{1/2})$. The convergence rate of the market risk is however $O_P((overline{Delta t})^{1/4})$. Based on $ilde{ho}$, the total risk is also studied, and it has the same convergence rate as that based on $hat{ho}$. 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.
展开▼
机译：在本草案中，我们考虑一种只涉及两个跳跃的资产价格过程的连续部分的对冲策略。套期保值策略的两个一致的估计值分别是已实现的双幂变化和阈值二次方变化，分别是$ hat { rho} $和$ tilde { rho} $。基于$ hat { rho} $，研究了操作风险，市场风险（由于跳跃而引起的风险）和总风险的估计量。事实证明，$ hat { rho} $的方差进入了操作风险估计量的偏差，而方差主要是由于跳跃影响了双功效估计误差。操作风险估算器的收敛速度（适当集中）为$ O_P（（ overline { Delta t}）^ {1/2}）$。但是，市场风险的收敛速度为$ O_P（（ overline { Delta t}）^ {1/4}）$。基于$ tilde { rho} $，还研究了总风险，并且其收敛速度与基于$ hat { rho} $的收敛速度相同。除了对金融计量经济学的兴趣外，当我们有兴趣估算相应的不可对冲残差过程的二次方差时，它在统计意义上也很重要。
展开▼
