在隨機波動模型具有因跳躍產生之不對稱效果下檢測價格是否跳躍──實證與模擬研究

Testing for Jumps in Prices under Jump-Driven Leverage Effect in Stochastic Volatility: An Empirical and Simulation Study

近年對價格跳躍的無母數檢測方法能在隨機波動模型具有因擴散性產生之不對稱效果下發揮效果。當不對稱效果的產生機制為價格與波動同時跳躍時，檢定價格跳躍的無母數方法表現則未知。本文為探討此一議題，透過模擬實驗進行兩隨機波動模型的比較。兩波動模型分別具有因擴散性與跳躍而產生之不對稱效果，但同時它們的參數經由實證數據產生，而使兩模型有近似相等的邊際分配。實驗結果顯示，文獻中一種常用的回顧型檢測方法，因受到跳躍產生之不對稱效果的影響，對所有的價格跳躍與負數之價格跳躍，分別有3.5%與5%的檢定能力下降。而文中提出一個新的檢定價格跳躍的方法，其能保有正確的型一錯誤性質，並被使用來驗證實驗結果的可靠性。

Recent non-parametric tests for jumps in prices are robust against a diffusion-driven leverage effect in stochastic volatility. When the leverage effect is channelled via jumps, it is less clear about the size and power properties of existing jump detection methods. To investigate this issue, a simulation study is conducted using two stochastic volatility models in which one is purely diffusion-driven and the other can be motivated by jumps. The two volatility models are specified and calibrated such that their marginal distributions are approximately identical. Simulation results indicate that a backward-looking test sees its power decline by over 3.5% and 5% for all and negative price jumps due to jump-driven leverage effect. A new jump test which controls its size at nominal level is used to provide a robustness check.