變異數交換契約在隨機波動度和跳躍模型下的實證分析

Abstract

本研究提供了一個混和Heston的隨機波動度和Kou的雙指數跳躍模型的變異數交換契約評價公式。在此混和模型下，連續和離散的變異數履約價皆可經由計算推得。我們探討此混和模型和Merton的跳躍擴散和隨機波動度模型的比較。根據實證結果顯示，混和模型的均方差較Merton模型來的小。因此，我們聲稱此混和模型對於預測已實現波動度下是較為好的模型。

We propose a hybrid model of Heston’s stochastic volatility and Kou’s double exponential jumps for the pricing of variance swaps. The fair continuous variance strike and the fair discrete variance strike in the hybrid model are both derived. We investigate the hybrid model and the Merton jump-diffusion and stochastic volatility model. Empirical Analysis shows the MSE in the hybrid model is smaller than the Black-Scholes model and the Merton jump-diffusion and stochastic volatility model. As a result, we claim the hybrid model is the better model for predicting the realized volatility.