本研究探討已開發及新興國家股市與黃金期貨、西德州原油期貨及比特幣之間的波動外溢效果。研究期間為2012年1月3日至2021年8月31日，進行跨市場之過去衝擊與波動外溢效果分析，透過多變量VAR(1)-GARCH(1,1)模型發現：(1)跨市場之報酬傳遞效果，僅在新興市場有跨市場報酬連動效果，顯示黃金前期報酬與原油前期報酬會連動至新興國家股市，兩者均顯著正向影響。(2)跨市場之訊息衝擊外溢效果，已開發與新興國家股市前期非預期衝擊均會加劇黃金之波動度。而黃金、原油與比特幣形成相當微妙的關係，原油前期非預期衝擊增加會加劇比特幣之波動度，而比特幣前期非預期衝擊增加會加劇黃金之波動度，最後，黃金前期非預期衝擊增加卻是減緩原油之波動度。(3)跨市場之波動外溢效果，已開發與新興國家股市前期波動均會減緩黃金之波動度，黃金、原油與比特幣也形成相當微妙的關係，原油前期波動會減緩比特幣之波動度，而比特幣前期波動會減緩黃金之波動度，最後，黃金前期波動會減緩原油之波動度。
最後，以已開發國家股市及新興國家股市作為避險標的，估計股市與黃金期貨、原油期貨以及比特幣之最適權重、最適避險比率及避險效果。研究發現，已開發國家股市的投資人傾向選擇以黃金作為避險組合的比重最高，其次為比特幣，原油最低；而新興國家股市則為黃金最高，原油其次，比特幣最低。在危機發生期間，黃金之最適權重顯著上升，且權重最大值都落於新冠疫情期間，代表股票投資人傾向將較多資金移轉至黃金。最適避險比率在已開發及新興國家股市的排序最高為原油、黃金其次、比特幣最低，代表投資人利用黃金、比特幣來規避股票部位風險的成本低於原油，而黃金之最適避險比率在危機發生期間，均顯著上升，原油也有類似的情形，表示黃金與原油在危機期間的避險成本上升。在全期樣本當中，已開發與新興國家股市避險效果由高至低之資產依序最高為黃金、其次為原油、比特幣為最低。值得一提，黃金在危機發生期間，尤其是在新冠疫情期間避險效果顯著上升；而比特幣在歐債危機期間能提供有效之避險，但在新冠疫情期間則無法；原油除了在歐債危機期間與新興國家股市之投資組合能提供有效之避險，但與已開發國家股市及在新冠疫情期間則無法提供有效之避險。整體而言，在已開發及新興國家股市中，黃金期貨提供之避險效果最佳。

The aim of this research is to explore the volatility spillover effect among developed stock markets, emerging stock markets, gold futures, WTI crude oil futures and bitcoin. The sample period is from January 3, 2012 to August 31, 2021, daily. The results of multivariate VAR(1)-GARCH(1,1) model show：(1) Dealing with return transmission across markets, a significant positive unidirectional effect is found from gold and crude oil to the emerging stock markets, respectively.
(2) Regarding to the cross-market ARCH effects, the past shocks of developed stock markets and emerging stock markets have a heightening effect on the gold. The gold, crude oil and bitcoin form a rather delicate relationship, the past shocks of crude oil have a heightening effect on the bitcoin, the past shocks of bitcoin have a heightening effect on the gold, the past shocks of gold have a calming effect on the crude oil.
(3) Regarding to the cross-market GARCH effects, the past volatilities of developed stock markets and emerging stock markets have a calming effect on the gold. The gold, crude oil and bitcoin form a rather delicate relationship, the past volatilities of crude oil have a calming effect on the bitcoin, the volatilities of bitcoin have a calming effect on the gold, the volatilities of gold have a calming effect on the crude oil.
Finally, this research explores the optimal weight, hedge ratio and hedging effectiveness of developed stock markets and emerging stock markets with gold futures, crude oil futures and bitcoin. Investors in the developed stock markets tend to choose gold as the first priority to hedge risks, followed by bitcoin, with crude oil as the lowest. In the emerging stock markets, gold has the highest optimal weight, followed by crude oil and bitcoin. During the crisis, the optimal weight of gold rose significantly, and the maximum weight was during the COVID-19 pandemic period, representing the tendency of stock investors to invest more funds on the gold. The optimal hedge ratio in the developed stock markets and emerging stock markets are from high to low: gold, crude oil, bitcoin, representing the hedge costs of gold and bitcoin in stock portfolios are lower than crude oil for investors. The optimal hedge ratio of gold during the crisis have risen significantly, crude oil also has a similar pattern. In the full sample, the hedging effectiveness of developed stock markets and emerging stock markets with the assets from high to low are gold, followed by crude oil, bitcoin as the lowest. It is worth mentioning that the hedging effectiveness of gold rises significantly during the COVID-19 pandemic. The bitcoin can provide effective hedging in the European debt crisis, but not in the COVID-19 pandemic. The crude oil can not provide effective hedging except the emerging stock markets in the European debt crisis. Overall, gold futures are the best safe-haven asset for the developed stock markets and emerging stock markets.

中文文獻
周慧冠(2021) ，比特幣與金融資產之連動關係，國立臺北大學統計學系碩士論文
林楷文(2020)，比特幣、黃金、美元指數波動傳遞效果分析:多變量BEKK模型之應用，國立高雄科技大學國際企業系碩士論文
曾羽榕(2020)，美國S&P500股價指數與黃金、原油期貨、美元指數間之波動外溢效果及避險效果探討，國立臺北商業大學財務金融研究所碩士論文
熊建至(2016)，石油價格與黃金價格之關聯性分析，大葉大學國際企業管理學系碩士班碩士論文
蘇坤豐(2017)，黃金、原油、美元指數與S&P500之關聯性分析，銘傳大學財務金融學系碩士在職專班碩士論文
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