跳躍擴散與隨機波動模型下台指選擇權之評價－快速傅立葉轉換之應用

Abstract

本文旨在應用快速傅利葉轉換法針對跳躍－擴散、隨機波動及混合模型等修正後選擇權評價模型以選擇權評價誤差模式分別進行其樣本內模型配適度分析與樣本外預測能力分析。實證結果顯示相對於蒙地卡羅模擬法，跳躍－擴散、隨機波動及混合模型等修正後選擇權評價模型為顯著較優之臺指選擇權評價模型。樣本內模型配適度之評價誤差分析方面，其實證結果顯示大抵係以隨機波動模型或混合模型為顯著較優之臺指選擇權評價模型。樣本外預測能力之評價誤差分析方面，1日樣本外預測除次近月選擇權外，整體、近月及遠月選擇權大抵亦以隨機波動模型或混合模型為顯著較優之臺指選擇權評價模型，其中買權與賣權大抵分別以隨機波動模型及混合模型為顯著較優之臺指選擇權評價模型。5日、10日及20日樣本外預測中，買權大抵係以混合模型為顯著相對較優之臺指選擇權評價模型，而賣權則係以隨機波動模型及混合模型為顯著相對較優之臺指選擇權評價模型。

The purpose of this study is to apply fast Fourier transform to investigate in-sample goodness of fit and out-of-sample prediction performance of three modified options pricing models, including jump-diffusion model, stochastic volatility model and stochastic volatility with jump model, through options pricing error analysis. The overall empirical results indicate that three modified options pricing models outperform Monte Carlo simulation method through the analysis of in-sample goodness of fit and out-of-sample prediction performance. The empirical results of in-sample goodness of fit indicate that the stochastic volatility and stochastic volatility with jump models are significantly superior pricing models of TAIEX index options. The empirical results of one-day out-of-sample prediction performance reveal that in addition to next-near-month options contracts, the stochastic volatility and stochastic volatility with jump models also are significantly superior pricing models of TAIEX index options of overall, near-month and far-month options contracts. The stochastic volatility and stochastic volatility with jump models are significantly superior pricing models of TAIEX index options for call and put options, respectively. Finally, the empirical results of five-day, ten-day and twenty-day out-of-sample prediction performance indicate that the stochastic volatility with jump model is significantly superior pricing model of TAIEX index options for calls, while the stochastic volatility and stochastic volatility with jump models are significantly superior pricing models of TAIEX index options for puts.