Heston隨機波動模型下對短到期隱含波動率曲面之校準

Abstract

本文旨在研究在Heston模型之下的對隱含波動率曲面校準問題。論文主要由兩個部分組成：首先，我們提出一個兩階段校準程序，有效地結合了來自現貨市場和衍生品市場的訊息。其次，我們聚焦於使用重要抽樣法評價短到期的歐式期權價格。此外，我們對重要抽樣的估計式進行了詳盡的變異數分析，並且顯示在Black-Scholes模型之下，估計式在大偏差理論下是漸近最佳的。

This paper addresses the calibration problem of the implied volatility surface within the framework of the Heston model. It comprises two main parts: firstly, we introduce a two-stage calibration procedure that effectively combines information from both the spot market and the derivative market. Secondly, we focus on the valuation of European options with short maturities, employing the importance sampling technique. Furthermore, we conduct a thorough variance analysis of our importance sampling estimator and show that it is asymptotically optimal under the Black-Scholes case by means of Large Deviation Principle.