COVID-19 前後S&P 500指數報酬之風險中立機率分配動差的比較分析

Abstract

本論文將COVID-19 大流行 前後的S&P 500 指數選擇權的IV曲面以Zhang 和 Xiang 的方法量化後轉而代表隱含風險中立分配的動差，我們將這些動差以不同選擇權到期時間長度做區分，可由此看出疫情前後市場對長短期市況預期的轉變。接著我們再將這些動差用Gehricke 和 Zhang 的方法轉換成時間序列，將動差的時間序列與VIX指數用VAR模型與共整合檢定一起查看比較，結果發現疫情期間隱含風險中立分配的三階和四階動差與VIX指數有較強的關聯性。以上的發現能夠幫我們更完善未來對S&P 500 指數報酬分配，應對金融大事件應有的設定。

This thesis quantifies the implied volatility surfaces of S&P 500 index options before and after the COVID-19 pandemic using the method proposed by Zhang and Xiang. Subsequently, these quantifications are represented as the moments of the implied risk-neutral distributions. We categorize these moments based on various time to maturities of options, which reveals the market''s changing expectations for short-term and long-term conditions before and after the pandemic. Furthermore, we convert these moments into a time series using the method of Gehricke and Zhang, and compare them with the VIX index using a VAR model and the cointegration test. The results show a strong correlation between the skewness and kurtosis of the implied risk-neutral distributions and the VIX index during the pandemic. These findings enhance our understanding of the S&P 500 index return distributions under significant financial distress.