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不懂別玩選擇權 - 希臘字母Greeks - Theta篇(一)



2012年11月,交易市場最大的改變就是周選擇權加掛制度的產生,
許多人發現近幾月台指振福大大降低,這已經將許多台指當沖客請出市場,
周選擇權想必吸引了台灣這個淺灘的市場更多的資金,在資金分散的狀況之下,
操作的難度提升了,這個難度的提升指的是知識門檻的提高,
那什麼是進入選擇權市場所需具備的基礎知識,
狼打團隊內牧清華推出選擇權的希臘字母系列,
提供大家ㄧ些進入選擇權市場前的暖身運動。




資料來源:永豐eleader

上圖是2013/03/29(禮拜五)201304W1(四月第一週)週選擇權收盤報價
加權指數收在7918,4月期貨收在7923,
我們只看選擇權的買權(Call)就好,
先看7900履約價的買權,成交價為47。

內涵價值

我們來舉個例子:假設要賣出7900Call在47點
換句話說,賣出ㄧ檔7900Call賣在47,效果類似於在7947點放空ㄧ口小台期貨
(前提假設是三天後結算在7900以上)
如果現在這個瞬間 ”當下” 就結算,由於加權為7918,所以7900Call理論上應該只有18點的價值(這稱為內涵價值)。

時間價值

7900Call現在卻有47點,高出內涵價值29點。
如果我們賣出7900Call在47點,等於多賣了7947-7918=29點(這稱為時間價值)。

換句話說,這多賣的29點,或是說高出來的29點,
根據選擇權的定義,是在未來三天內要「ㄧ定要消失的」
(2013.04.01 (周ㄧ)、2013.04.02(周二)、2013.04.03(周三))
因此我們可以推估..以平均而言,每一天約消失29/3點(湊整數算10點),
當然實際上不是這樣,這邊說的是「以平均而言」。
要注意到的是,越接近結算,「以平均而言」這句話越能接近「實際情形」
因為平均 = 總共消失的點數/剩餘天數
剩餘天數越少代表除下去的結果越接近實際每天消失的點數。
也就是說距離結算只剩短短三天了,這以「平均而言」, 每天就是該消失10點。

以上這段如果讀者你看得懂,那恭喜你,你已經初步了解什麼是Theta了:
結論:Theta的定義是每接近結算日一天,選擇權價值流失的點數

所以這裡的Theta應該可以估計是10。雖然理論計算出來的只有5,個人認為這數字因為接近結算日的關係失真了,這裡我必須指出,越接近結算日,希臘字母越失真!再換句話說,如果未來三天大盤指數都不動的話,那只要賣出7900Call在47點,每天在家躺著就賺到10點,新台幣500元入袋。天底下有這麼好康的事? 就是真的有!但也可以說沒有;因為有個前提假設是 “三天過後指數要結算在7918以下”

我們來看ㄧ下所有可能發生的情形,首先先看結算在7918之下的情形:
  • Case 1:若指數三天後結算在7918,那的確是每天穩穩的賺到10點500元。三天後賺到1500元。
  • Case 2:若指數三天後結算在7900~7918,那賣出7900Call在47點至少賺到29點再加上7918往下跌的點數。例如結算在7910(7918往下跌8點)則賺到29+8=37點。
  • Case 3:若指數三天後結算在7900之下,那恭喜了!賣出 7900Call在47點全收,47點歸零,約賺到2300元(扣手續費後)。

    由上面的分析可知:只要指數結算在7918以下,29點的時間價值是穩穩收到口袋的。
再來看結算在7918之上的情形:
  • Case 4: 如果是結算在7918~7947。那還是恭喜,你還是賺到!賺到多少?賺到穩賺的29點扣掉7918往上漲的點數(例如結算在7930,也就是7918往上漲12點,那就賺到29-12=17點)
  • Case 5: 如果是結算在7947之上,那要小心開始賠錢了。賠多少?就看7947往上漲多少點了?假設結算在7960點,那就賠了7960-7947=13點。

可以注意到的是,7918~7947可以說是你的護城河(有29點的保護空間,也就是這三天該消失的時間價值29點,賣出7900Call是 “看不漲”,然而實際情形卻漲了,你看錯卻不會賠到錢,甚至還有可能賺到錢,這樣乍看好像是ㄧ件很吸引人的投資。

從上面例子可以看出,單純裸賣7900Call在47點,Case 1~Case 4都是會賺錢的,或著說現在大盤7918點,只要不漲超過7947點都是會賺錢的,但最多就是賺到47點。

恐怖的是, 萬ㄧ漲超過7947點,開始會賠錢,風險無限,漲超過7947多少點,就賠多少點。等同於在7947放空ㄧ口小台期貨卻一路被嘎上去! 遇到這種情形,那真的要非常小心,期權市場多少英雄豪傑都是死在這種情形,以為發生的機率很低,然而卻發生了,黑天鵝,讓你一路賠很大!而裸賣選擇權,也是非常不建議的方式,這個例子只是希望大家能夠簡單的了解希臘字母Theta的意思。

Theta:每接近結算日一天,選擇權價值流失的點數。

如果今天你認為三天後大盤結算的機率分佈如下:
收在7947之下有80%,收在7947之上有20%,那你該怎麼做?
如果收在7947之下有60%,收在7947之上有40%,你又該怎麼做?
請按讚支持狼打專欄,未來即將推出【資金控管的藝術】。

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