This study tests if historical volatility- and implied volatility has significant predictive power over future realized volatility and if so which one of the two is the superior predictor. The study is conducted by using historical volatility of the OMXS30 and implied volatility from OMXS30 call options during the period 2012-2023. Three regressions have been made to test the research questions, two simple linear regression and one multiple linear regression. The results of the study showed that both historical- and implied volatility had significant predictive power over future realized volatility with implied being the superior one with a higher correlation coefficient. The multiple regression showed that both the independent variables were important and both of them explained different parts of the data, which means that they have complementary abilities and that both should be used when assessing the forecast of realized volatility.

Master of Science / Department of Agricultural Economics / Glynn Tonsor / This decade has seen movements in commodity futures markets never seen before. There are many factors that have intensified price movements and volatility behavior. Those factors likely altering supply and demand include governmental policy within and outside of the U.S, weather shocks, geopolitical conflicts, food safety concerns etc. Whatever the reasons are for price movements it is clear that the volatility behavior in commodity markets constantly change, and risk managers need to use current and efficient tools to mitigate price risk. This study identified market structural breaks of realized volatility in corn, wheat, soybeans, live cattle, feeder cattle and lean hogs futures markets. Furthermore, this study analyzes the forecasting performance of implied volatility, historical volatility, a composite approach and a naïve approach as forecasters of realized volatility. The forecasting performance of these methods was analyzed in the full period of time of our weekly data from January 1995 to April 2014 and in each identified market regime for each commodity. Previous research has analyzed forecasting performance of implied volatility, a time series alternative and a composite method. However, to the best of my knowledge, they have not worried about market structural breaks in the data that might influence the performance of the mentioned forecasting methods in different periods of time. Overall, results indicate that indeed there are multiple market structural breaks present in the volatility datasets across all six commodities. We found differences in the forecasting performance of the analyzed methods when individual market regimes were analyzed. There seems to be evidence that corroborates the idea in the literature about the superiority of implied volatility over a historical volatility, a composite approach and a naïve approach. Additionally, implied volatility encompassed all the information contained in the historical volatility and the naïve measure across each identified market regime in all six commodities. Our results show that when both implied volatility and historical volatility are available, the benefit of combining those measures into a composite forecasting approach is very limited. Our results hold true for a short term 1 week ahead realized volatility forecast. It would be of interest to see how results vary for longer forecasting time horizons.

Many past literatures have examined the predictive power of implied volatility versus that of historical volatility, but they have showed divergent conclusions. One of the major differences among these studies is the methods that they used to obtain implied volatility. The VIX index, introduced in 1993, provides a model-free and directly observable source of implied volatility data. The VIX futures is an actively traded VIX derivative product, and its prices are believed to contain market’s expectation about future volatility. By analyzing the relationship between the VIX futures prices and the realized volatilities of the 30-day period that these VIX futures contracts cover, this paper finds that the VIX futures contracts with shorter maturities have predictive power on future realized volatility, but they are upwardly biased estimates. The predictive power, however, decreases as the time to maturity increases. The outstanding VIX futures contracts with the nearest expiration dates outperform GARCH estimates based on historical return data at predicting future realized volatility.

本研究有系統地收集了2003年8月12日到2005年9月30日止共495個交易日的台指期貨、選擇權市場裡P/C量、P/C倉、隱含波動率(AIV)、不同天數的歷史波動率等收盤資料，進行這些因素與行情走勢間的關係，以及因素彼此的互動性。結果證實分析台指選擇權指標是需要區分金融重大衝擊前後期間，以及區分漲勢、跌勢、盤整的各期間，各期間的選擇權指標均會有不同意涵。 本論文證實使用結構轉換的Chow-ARMA(2,1)模型可能比較符合模擬指數 實況，且GARCH(1,1) 模型也很適合描述台期指貨波動度預測力。在選擇權指標方面：P/C量與AIV與台指期貨呈現負相關，P/C倉與台指期貨正相關。其中以P/C倉對指數漲跌的影響程度最大、P/C量的影響程度次之、AIV影響程度最小。若把隱含波動率區分成買權與賣權之各個波動率更有效地預測行情走勢，在大跌期間的買賣權隱含波動率更能表現出優越的預測能力，其中前兩期的賣權隱含波動率(PIV)更是效率性指標， 實證結果使用20天的歷史波動率比較能貼近選擇權市場的變化，跟過去教 科書慣用的90天不同。若比較歷史波動率與隱含波動率間的關係，結論是當「大跌期」歷史波動率大於買權隱含波動率(CIV)時，買權是會被低估的，其他的各種假設條件均不成立。理由有二：一是市場效率性決定了是否可使用隱含波動率與歷史波動率之間的高低關係。二是「大跌時期」相對於「大漲時期」的市場資訊被反應的更敏銳，而在「大跌時期」的賣權價格反應比買權價格反應更快速敏銳。 本研究推論的Chow-ARMA(2,1) 台指期貨模型、GARCH(1,1) 波動率模型、P/C量-P/C倉-AIV的多變數模型、FMA20/XIV模型等等在研判指數變化上具有參考價值，進一步均可以做為選擇權操作策略參考依據之一。