具跳躍的隨機波動模型之台指選擇權市場實證

Abstract

本論文以具跳躍的隨機波動模型之各種變形進行探討，以台指選擇權市場作 為研究對象。我們檢驗 Heston 模型在短天期下是否無法良好捕捉市場的隱含波動 度，並分析在價格具跳躍的 Bates 模型以及價格和波動度同時具跳躍的 SVJJ 模型 可以對短天期提升多少的校準精準度。此外，我們討論了模型校正，比較不同演 算法及校正方式下之的校準誤差，從而提出適用台指選擇權市場的校正方法。研 究顯示 Bates 模型可以大幅改善 Heston 短天期的校準誤差，且即使在波動劇烈時 也有理想的校準能力，然而，SVJJ 模型在校正時間大幅提高下卻無法帶來顯著的 精準度提升。同時，我們建構交易策略，檢驗了三個模型在樣本外的獲利表現， 結果與樣本內一致。

Our study investigates various modifications of stochastic volatility models with jumps, using the Taiwan Index Options market as the research subject. We examine whether the Heston model fails to capture the market’s implied volatility well for short maturities and analyze how much the Bates model and the SVJJ model with contempo- raneous price and volatility jumps can improve calibration accuracy for short maturities. Additionally, we discuss model calibration, comparing calibration errors under different algorithms and calibration methods, and propose a calibration method suitable for the Taiwan Index Options market. The research shows that the Bates model significantly im- proves the calibration errors of the Heston model for short maturities and maintains ideal calibration performance during periods of high volatility. However, the SVJJ model does not provide significant accuracy improvement despite a substantial increase in calibra- tion time. Meanwhile, we constructed trading strategies and examined the out-of-sample profitability of the three models, with results consistent with in-sample performance.