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第三節 波動率關聯分析
一般而言，掌握趨勢的脈動是投入金融商品市場所應具備的思維，其中尤以波動 率更是金融商品非常重要的一項指標。因為，透過波動率的漲跌現象，可以清楚作出 金融交易的決定，例如投資者是應該決決定做買方或是賣方。而波動率的計算又可分 為歷史波動率、隱含波動率及未來波動率三種，本研究僅針對歷史波動率的計算來探 討台股指數現貨收盤價與台指選擇權賣方清算權益值等交易的波動情況，其中歷史波 動率區分為五日波動率、十日波動率及二十日波動率等三類進行研究分析，並分述如 下：
一、 五日波動率
五日波動率是過去的五日為一時段，分別計算台股指數現貨收盤價與台指選擇權 賣方清算權益值的年化報酬率標準差，其結果如表4-2。
表 4- 4 台股指數收盤價與選擇權賣方清算權益值之五日波動率 日期 現貨收盤價 清算權益值 日期 現貨收盤價 清算權益值 1040112 24.05% 91.02% 1040508 8.57% 21.09%
1040113 13.40% 85.15% 1040511 7.28% 15.63%
1040114 15.08% 80.71% 1040512 8.29% 8.19%
1040115 7.00% 87.98% 1040513 9.76% 7.91%
1040116 7.04% 76.08% 1040514 9.78% 29.59%
1040119 7.60% 73.08% 1040515 9.80% 30.45%
1040120 8.98% 75.14% 1040518 10.40% 33.00%
1040121 8.16% 67.88% 1040519 13.84% 32.10%
1040122 7.08% 62.00% 1040520 13.61% 42.75%
1040123 4.24% 61.22% 1040521 13.30% 30.96%
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1040126 6.02% 58.49% 1040522 13.84% 32.72%
1040127 5.86% 56.20% 1040525 13.77% 33.30%
1040128 7.32% 53.84% 1040526 10.49% 23.07%
1040129 11.51% 64.53% 1040527 10.50% 24.86%
1040130 8.80% 62.03% 1040528 3.32% 22.73%
1040202 9.32% 55.54% 1040529 2.52% 14.00%
1040203 10.23% 48.69% 1040601 7.01% 11.60%
1040204 11.88% 88.85% 1040602 6.51% 10.83%
1040205 9.02% 83.28% 1040603 6.32% 10.59%
1040206 8.40% 84.49% 1040604 13.55% 49.34%
1040209 9.25% 80.49% 1040605 13.65% 150.16%
1040210 7.83% 80.61% 1040608 15.57% 148.20%
1040211 8.09% 6.94% 1040609 17.54% 162.58%
1040212 8.77% 7.14% 1040610 22.99% 161.97%
1040213 7.46% 7.15% 1040611 17.75% 141.66%
1040224 7.94% 9.12% 1040612 17.77% 62.88%
1040225 4.63% 11.88% 1040615 17.55% 54.31%
1040226 11.07% 12.84% 1040616 10.61% 102.04%
1040302 11.73% 13.13% 1040617 3.99% 106.15%
1040303 11.71% 12.67% 1040618 5.37% 106.28%
1040304 8.86% 12.69% 1040622 12.18% 105.45%
1040305 5.95% 12.51% 1040623 11.40% 93.36%
1040306 5.13% 7.43% 1040624 9.47% 36.96%
1040309 8.31% 6.14% 1040625 7.79% 29.96%
1040310 8.31% 4.57% 1040626 9.41% 34.41%
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1040311 7.86% 4.49% 1040629 20.41% 58.40%
1040312 10.34% 4.40% 1040630 21.54% 60.96%
1040313 9.24% 4.13% 1040701 22.12% 61.15%
1040316 8.46% 5.15% 1040702 20.80% 61.30%
1040317 8.67% 8.90% 1040703 20.79% 61.33%
1040318 11.81% 9.94% 1040706 12.40% 27.61%
1040319 12.08% 9.93% 1040707 9.57% 18.59%
1040320 11.52% 100.45% 1040708 20.27% 48.23%
1040323 7.76% 100.99% 1040709 18.80% 64.22%
1040324 9.56% 107.75% 1040713 25.14% 76.51%
1040325 8.93% 106.99% 1040714 25.38% 72.27%
1040326 5.56% 107.59% 1040715 25.62% 71.95%
1040327 7.61% 72.04% 1040716 11.77% 64.17%
1040330 8.15% 74.89% 1040717 9.38% 39.72%
1040331 11.74% 8.81% 1040720 6.05% 28.35%
1040401 12.11% 9.63% 1040721 6.85% 28.75%
1040402 14.98% 10.22% 1040722 8.88% 38.15%
1040407 10.90% 11.80% 1040723 11.72% 33.67%
1040408 13.14% 9.24% 1040724 10.89% 34.03%
1040409 12.12% 9.70% 1040727 17.02% 34.66%
1040410 10.23% 8.25% 1040728 16.82% 17.78%
1040413 8.51% 8.41% 1040729 17.62% 15.43%
1040414 8.40% 6.69% 1040730 20.53% 52.25%
1040415 10.35% 3.81% 1040731 20.82% 56.72%
1040416 13.82% 4.21% 1040803 15.62% 67.46%
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1040417 15.24% 3.27% 1040804 15.25% 67.23%
1040420 14.27% 3.37% 1040805 15.69% 68.59%
1040421 14.28% 4.01% 1040806 13.63% 44.91%
1040422 13.56% 6.82% 1040807 13.01% 46.03%
1040423 17.30% 45.09% 1040810 9.23% 27.24%
1040424 14.37% 138.70% 1040811 10.59% 32.14%
1040427 12.22% 139.57% 1040812 10.93% 29.31%
1040428 12.03% 136.75% 1040813 11.71% 32.59%
1040429 18.17% 131.14% 1040814 11.72% 46.65%
1040430 13.65% 93.02% 1040817 11.31% 46.58%
1040504 9.91% 36.54% 1040818 11.10% 46.29%
1040505 7.43% 37.19% 1040819 14.17% 48.53%
1040506 7.68% 39.41% 1040820 13.18% 49.71%
1040507 8.49% 18.41% 1040821 19.84% 161.46%
根據表4-2所顯示的結果，在台股指數現貨收盤價的部分，以民國104年8月為例，
波動率多數超過10%以上，從8月20日(當日收盤價為8,030元)的13.18%來看，顯示台股 指數現貨收盤價一年之後的預估會介在6,972元~9,088元之間，若以月來看8月20日的 五日波動率則為3.8%，表示台股指數現貨收盤價一個月後預估會介在7,725元~8,335元 間。同樣地，在選擇權賣方清算權益值的五日波動率中，亦是呈現大幅度的波動現象，
而且當台股指數現貨收盤價的五日波動率較小時，清算權益值的五日波動率則會同時 也變低，反之若台股指數現貨收盤價的五日波動率較大時，清算權益值的五日波動率 則會同時也變高。因此，在此一五日波動率的現象發生下，表示台股指數現貨收盤價 與台指選擇權賣方清算權益值是存在著一個參考價值的關係。
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二、 十日波動率
十日波動率是過去的十日為一時段，分別計算台股指數現貨收盤價與台指選擇權 賣方清算權益值的年化報酬率標準差，其結果如表4-3。
表 4- 5 台股指數收盤價與選擇權賣方清算權益值之十日波動率 日期 現貨收盤價 清算權益值 日期 現貨收盤價 清算權益值 1040119 16.89% 78.06% 1040513 8.31% 34.69%
1040120 11.17% 75.75% 1040514 8.69% 27.65%
1040121 11.45% 71.20% 1040515 8.68% 28.74%
1040122 8.32% 71.86% 1040518 8.72% 26.15%
1040123 9.20% 65.11% 1040519 11.17% 23.91%
1040126 8.50% 63.03% 1040520 11.21% 29.43%
1040127 8.42% 62.68% 1040521 11.05% 29.48%
1040128 7.36% 59.08% 1040522 11.69% 35.31%
1040129 9.40% 59.91% 1040525 11.63% 36.90%
1040130 10.25% 58.34% 1040526 11.67% 36.94%
1040202 10.22% 60.15% 1040527 11.49% 37.01%
1040203 9.95% 56.71% 1040528 9.58% 28.11%
1040204 9.88% 69.98% 1040529 9.38% 23.90%
1040205 9.76% 70.30% 1040601 10.35% 25.51%
1040206 8.88% 70.26% 1040602 8.23% 22.67%
1040209 9.03% 68.67% 1040603 8.55% 20.19%
1040210 8.60% 64.05% 1040604 12.75% 43.55%
1040211 9.63% 64.76% 1040605 11.86% 101.14%
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1040213 7.50% 64.04% 1040609 14.09% 109.66%
1040224 8.68% 62.73% 1040610 16.05% 109.54%
1040225 8.77% 57.74% 1040611 15.90% 109.56%
1040226 9.87% 9.73% 1040612 15.97% 109.54%
1040302 9.99% 11.14% 1040615 15.85% 110.46%
1040303 9.26% 11.90% 1040616 15.78% 128.48%
1040304 8.79% 11.83% 1040617 15.77% 129.17%
1040305 8.76% 12.06% 1040618 12.39% 118.54%
1040306 8.48% 11.31% 1040622 14.43% 86.23%
1040309 9.90% 9.77% 1040623 14.60% 85.63%
1040310 9.91% 9.11% 1040624 9.92% 73.21%
1040311 8.05% 9.00% 1040625 9.19% 73.62%
1040312 8.16% 9.07% 1040626 9.32% 74.70%
1040313 7.22% 6.26% 1040629 16.06% 87.13%
1040316 7.91% 5.49% 1040630 16.64% 85.02%
1040317 8.10% 6.96% 1040701 16.47% 50.96%
1040318 10.27% 8.15% 1040702 16.32% 50.06%
1040319 10.88% 7.44% 1040703 16.44% 50.61%
1040320 10.67% 70.01% 1040706 16.08% 44.46%
1040323 9.22% 70.07% 1040707 15.71% 43.14%
1040324 9.21% 81.96% 1040708 21.16% 54.67%
1040325 10.08% 82.54% 1040709 19.89% 59.77%
1040326 9.93% 82.50% 1040713 22.12% 69.04%
1040327 11.70% 82.58% 1040714 19.31% 54.40%
1040330 11.23% 84.11% 1040715 18.37% 53.90%
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1040331 11.67% 83.40% 1040716 17.79% 53.67%
1040401 10.48% 83.57% 1040717 17.79% 54.15%
1040402 10.79% 83.50% 1040720 17.89% 54.84%
1040407 11.10% 52.13% 1040721 17.82% 53.25%
1040408 11.45% 52.06% 1040722 18.11% 59.12%
1040409 11.46% 9.15% 1040723 12.56% 53.06%
1040410 11.58% 9.29% 1040724 12.28% 47.74%
1040413 11.58% 9.29% 1040727 13.88% 35.80%
1040414 9.48% 9.14% 1040728 14.19% 33.24%
1040415 11.24% 7.35% 1040729 13.83% 30.68%
1040416 12.40% 7.31% 1040730 15.89% 41.56%
1040417 12.54% 6.27% 1040731 16.00% 44.25%
1040420 11.51% 6.31% 1040803 17.07% 50.58%
1040421 11.20% 5.65% 1040804 16.54% 46.44%
1040422 11.52% 5.54% 1040805 16.98% 47.69%
1040423 14.79% 33.28% 1040806 16.48% 48.87%
1040424 15.49% 93.48% 1040807 16.54% 49.27%
1040427 15.53% 95.78% 1040810 12.10% 49.13%
1040428 15.45% 96.66% 1040811 12.41% 49.84%
1040429 15.38% 98.82% 1040812 13.60% 51.09%
1040430 14.83% 98.41% 1040813 12.04% 38.19%
1040504 13.60% 97.34% 1040814 11.79% 44.51%
1040505 13.67% 96.35% 1040817 10.50% 35.99%
1040506 13.52% 95.56% 1040818 10.44% 37.71%
1040507 14.96% 95.58% 1040819 11.93% 39.42%
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1040508 11.05% 82.26% 1040820 12.13% 39.97%
1040511 8.42% 41.35% 1040821 17.35% 121.08%
1040512 7.42% 38.21%
根據表 4-3 所顯示的結果，在台股指數現貨收盤價的部分，以民國 104 年 8 月為 例，波動率多數超過 10%以上，從 8 月 20 日(當日收盤價為 8,030 元)的 12.13%來看，
顯示台股指數現貨收盤價一年之後的預估會介在 7,056 元~9,004 元之間，若以月來看 8 月 20 日的十日波動率則為 3.5%，表示台股指數現貨收盤價一個月後預估會介在 7,749 元~8,311 元間。由於十日波動率是站在中間時段點的角度，觀察台股指數現貨 收盤價的波動，在選擇權賣方清算權益值的十日波動率中，亦是呈現與五日波動率相 似的趨勢，也就是說，當台股指數現貨收盤價的十日波動率較大時，清算權益值的十 日波動率隨之提高，反之亦然。所以，在台股指數現貨收盤價十日波動率的變動，將 是成為台指選擇權賣方所能參考的指標之一。
三、 二十日波動率
二十日波動率是過去的二十日為一時段，分別計算台股指數現貨收盤價與台指選 擇權賣方清算權益值的年化報酬率標準差，其結果如表4-4。
表 4- 6 台股指數收盤價與選擇權賣方清算權益值之二十日波動率 日期 現貨收盤價 清算權益值 日期 現貨收盤價 清算權益值 1040202 13.87% 68.23% 1040520 12.58% 74.88%
1040203 10.29% 67.08% 1040521 12.93% 74.64%
1040204 10.42% 68.73% 1040522 11.08% 68.74%
1040205 8.83% 69.22% 1040525 10.07% 41.06%
1040206 9.11% 65.93% 1040526 9.80% 37.98%
1040209 9.08% 65.16% 1040527 9.90% 35.72%
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1040210 9.04% 65.68% 1040528 9.36% 27.68%
1040211 8.97% 62.48% 1040529 9.31% 27.56%
1040212 8.92% 62.11% 1040601 9.56% 26.92%
1040213 8.76% 60.47% 1040602 9.55% 26.36%
1040224 9.23% 60.30% 1040603 9.70% 26.31%
1040225 9.14% 56.70% 1040604 11.65% 36.32%
1040226 9.64% 57.11% 1040605 11.66% 74.66%
1040302 9.62% 57.01% 1040608 11.77% 75.55%
1040303 8.94% 53.91% 1040609 13.22% 79.82%
1040304 8.95% 51.17% 1040610 13.94% 79.94%
1040305 8.91% 46.21% 1040611 13.50% 77.94%
1040306 9.05% 46.30% 1040612 13.50% 77.19%
1040309 9.02% 45.39% 1040615 13.45% 78.06%
1040310 8.66% 45.36% 1040616 12.53% 90.71%
1040311 8.68% 44.84% 1040617 12.53% 91.08%
1040312 8.78% 40.82% 1040618 12.26% 90.90%
1040313 8.51% 8.94% 1040622 13.11% 91.56%
1040316 8.90% 9.13% 1040623 13.32% 91.67%
1040317 8.67% 9.53% 1040624 13.26% 91.68%
1040318 9.41% 9.89% 1040625 13.65% 91.44%
1040319 9.62% 9.81% 1040626 13.60% 91.67%
1040320 9.40% 49.81% 1040629 15.85% 96.37%
1040323 9.37% 49.48% 1040630 16.25% 96.33%
1040324 9.45% 59.06% 1040701 16.44% 96.16%
1040325 9.13% 59.36% 1040702 16.36% 96.05%
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1040326 8.91% 59.58% 1040703 14.36% 90.96%
1040327 9.47% 59.15% 1040706 14.89% 68.26%
1040330 9.49% 59.82% 1040707 14.83% 67.46%
1040331 9.82% 59.94% 1040708 17.01% 64.58%
1040401 10.21% 60.28% 1040709 16.43% 67.70%
1040402 10.80% 60.37% 1040713 17.31% 70.80%
1040407 10.75% 60.24% 1040714 17.32% 70.75%
1040408 10.61% 60.22% 1040715 17.31% 69.33%
1040409 10.56% 60.36% 1040716 17.25% 51.87%
1040410 10.69% 60.59% 1040717 17.24% 51.33%
1040413 10.50% 60.57% 1040720 17.35% 52.13%
1040414 10.53% 60.62% 1040721 16.59% 50.46%
1040415 10.94% 60.83% 1040722 16.59% 52.00%
1040416 11.72% 60.59% 1040723 17.06% 52.46%
1040417 11.39% 60.48% 1040724 16.49% 53.20%
1040420 10.88% 60.56% 1040727 17.98% 53.82%
1040421 10.86% 37.16% 1040728 16.68% 46.45%
1040422 11.34% 37.52% 1040729 15.97% 46.78%
1040423 13.30% 24.88% 1040730 16.43% 50.00%
1040424 13.62% 64.98% 1040731 16.48% 52.20%
1040427 13.51% 67.08% 1040803 17.04% 56.39%
1040428 12.56% 68.29% 1040804 16.90% 56.30%
1040429 13.35% 70.78% 1040805 17.09% 56.14%
1040430 13.33% 70.70% 1040806 14.34% 52.06%
1040504 12.85% 70.36% 1040807 14.28% 49.81%
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1040505 12.58% 70.23% 1040810 13.16% 42.45%
1040506 12.53% 70.30% 1040811 13.20% 41.88%
1040507 13.00% 70.79% 1040812 13.47% 41.19%
1040508 13.01% 70.98% 1040813 13.72% 40.13%
1040511 12.96% 70.91% 1040814 13.68% 43.22%
1040512 12.85% 70.97% 1040817 13.84% 43.21%
1040513 12.90% 70.96% 1040818 13.53% 41.72%
1040514 13.03% 73.57% 1040819 14.37% 42.62%
1040515 12.30% 74.45% 1040820 14.11% 43.60%
1040518 11.92% 74.32% 1040821 16.87% 91.69%
1040519 12.54% 74.88%
根據表 4-4 所顯示的結果，在台股指數現貨收盤價的部分，以民國 104 年 8 月為 例，波動率多數超過 10%以上，從 8 月 20 日(當日收盤價為 8,030 元)的 14.11%來看，
顯示台股指數現貨收盤價一年之後的預估會介在 6,897 元~9,163 元之間，若以月來看 8 月 20 日的二十日波動率則為 4.1%，表示台股指數現貨收盤價一個月後預估會介在 7,701 元~8,359 元間。然而，由於二十日波動率是看較長時間的波動，整體的波動幅 度也傾向平穏許多，也是漲跌幅度也相對小，故在選擇權賣方清算權益值的二十日波 動率中，亦是呈現與五日波動率或十日波動率有相似的走勢，換言之，當台股指數現 貨收盤價的二十日波動率變大時，清算權益值的二十日波動率隨之升高，相反地，當 台股指數現貨收盤價的二十日波動率變小時，清算權益值的二十日波動率隨之降低。
因此，在台股指數現貨收盤價二十日波動率的變動，也可以成為台指選擇權賣方所能 參考的指標之一。
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第伍章 結論與建議
本章區分結論與建議等二節，於第一節整理闡述實證分析之主要結果與台股指數 現貨收盤價與台指選擇權賣方清算權益值之每日交易現況，並依分析結果擬訂建議事 項敘述於第二節。