波動度交易之風險與報酬-跳躍模型的應用

Abstract

本文使用多個模型來估計台灣選擇權市場的波動性，希望透過考慮隨時間變化的跳躍頻率(jump intensity)和跳躍規模(jump size)的GARJI模型，能在金融市場上有較好的表現。

除了GARJI模型外，我們也使用其他波動度模型（GARCH、GJR-T、EGARCH、歷史波動度、隱含波動率模型）一起比較對已實現波動率的預測能力。本文使用三種方式：第一種為均方根誤差(root of mean squared error)RMSE。第二種方式為：單一廻歸，檢驗其係數是否顯著，並且比較調整後的R-square。第三種方式為：包含廻歸，檢定增加的波動度是否可以增加對已實現波動度的解釋能力。根據我們的研究結果指出，GARJI模型不管是在單一廻歸和包含廻歸中，係數都相當顯著。

但是，要在金融市場上有良好的運用才是我們主要的目的。因此利用GARJI模型在波動度較佳的預測能力下trading Straddle，看其是否能在台灣選擇權市場上能否有好的獲利表現。結果顯示在未考慮手續費時，我們每天有平均2.8574%的日報酬率，但是考慮手續費後，日報酬率為2.6047%。

This paper considers the forecasting performance of volatility models with applications in options trading strategies in Taiwan option market. The results reveal that the GARJI model that considering jump intensity and jump size can help us with better performance in the financial market. We compare GARJI model with other models, such as GARCH, GJR-T, EGARCH, historical volatility and implied volatility, to examine which is better in prediction. The three methods to evaluate the performance of volatility forecast in this paper are Root of Mean Squared Error (RMSE), Univariate regression and Encompassing regression. According to our results, GARJI model not only has better ability to predict the volatility, but also gets more information content. Besides, by trading straddle, the average profits are 2.8574% and 2.6047% in Taiwan option market with and without transaction cost, respectively.