隨機波動效果下VIX及VIX商品之評價

本文主要專注於探討隨機波動效果對波動指數及波動度的衍生性商品之影響。我們分別對隨機波動模型下的VIX及VIX期貨做評價。實證研究上，我們利用一般動差法(GMM)及非線性最小平方法對評價模型進行兩階段參數估計，並將其與非線性估計法比較，發現以兩階段估計法所得的VIX模型在大部分的期間有不錯的配適效果，僅部分的極端值較容易偏離；在評價VIX期貨則僅低估0.09%至0.82%。其結果也顯示隨機波動風險對VIX及VIX期貨有明顯的影響。

關鍵字

隨機波動；衍生性商品； VIX ； VIX期貨；一般動差法；非線性最小平方法

並列摘要

The aim of this paper is to explore effects of the stochastic volatility for volatility index and volatility derivatives. We price VIX and VIX futures under stochastic volatility model. In empirical study, we use GMM and nonlinear least square method to estimate the parameters of the pricing model, and we compared the results with nonlinear method. The empirical study shows that the VIX model with parameters estimated from this procedure has a good fit on most of period, although some outliers perform not very well. While pricing VIX futures, we find that the discrepancy between the model price and market price is just 0.09% to 0.82% undervalued for the futures contracts. These results demonstrate that the stochastic volatility risk can have a significant effect on the VIX and VIX futures.

並列關鍵字

Stochastic volatility ； derivatives ； VIX ； VIX futures ； GMM ； nonlinear least square method

參考文獻

Google Scholar

(1). Andersen, T. G., & Sorensen, B. E. (1996). “GMM Estimation of a Stochastic Volatility Model: a monte carlo study.” Journal of Business and Economics Statistics, 14, 328-352.