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hyi725 · 2023年08月12日

时间点问题

  1. CFA III
  2. Derivative

* 问题详情，请 查看题干

NO.PZ201601050100001705

问题如下：

Based on the CFO’s set of assumptions, the gain on the purchase of the variance swap on the S&P 500 in five months would be closest to:

选项：

A.

$4,317,775.

B.

$4,355,556.

C.

$4,736,334.

解释：

A is correct.

The gain on the variance swap is calculated as:


Values for the inputs are as follows:

Volatility strike on existing swap = 15

Variance strike on existing swap = 152 = 225

Variance  Notional=Vega  Notional2×Strike=$1,000,0002×15=$33,333.33Variance\;Notional=\frac{Vega\;Notional}{2\times Strike}=\frac{\$1,000,000}{2\times15}=\$33,333.33

RealizedVol(0,t)2 = 202 = 400

ImpliedVol(t,T) 2 = 182 = 324

t = 5

T = 12

PVt(T)=11+[1.50%(712)]=0.991326PV_t\left(T\right)=\frac1{1+\left[1.50\%\left({\displaystyle\frac7{12}}\right)\right]}=0.991326

which is the present value interest factor after five months (i.e., discounting for seven remaining months, from t to T), where the annual interest rate is 1.50%.

Thus, the value of the swap in five months is calculated as follows:


Given that Monatize would be long the swap, the mark-to-market value would be positive (i.e., a gain) for Monatize, equal to $4,317,775.

中文解析：

本题考察的是variance swap。

求得是5个月后variance swap的value，比较简单，重点是记住上面的公式。

需要注意的是：

公式中的realized volatility，implied volatility以及strike代入数字的时候只取百分号前面的数字。

另外此公式求解的是站在long position的角度的value（也就是本题中的情景）；如果题目要求的是short position的value，需要加负号。

over the next 5 month, volatility is 20%，所以默认现在是时间点0开始在7个月吗？

老师可以画图一下吗

没明白为什么公式里减去X的平方是15的平方而不是减去18的平方

新的strike price不是18吗？

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1 个答案

pzqa31 · 2023年08月13日

嗨，从没放弃的小努力你好：


同学，请把题干贴一下，我看不到题干。

----------------------------------------------
努力的时光都是限量版，加油！

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NO.PZ201601050100001705 问题如下 Baseon the CFO’s set of assumptions, the gain on the purchase of the varianswon the S P 500 in five months woulclosest to: A.$4,317,775. B.$4,355,556. C.$4,736,334. A is correct. The gain on the varianswis calculateas:Values for the inputs are follows:Volatility strike on existing sw= 15Varianstrike on existing sw= 152 = 225Variance  Notional=Vega  Notional2×Strike=$1,000,0002×15=$33,333.33Variance\;Notional=\frac{Vega\;Notional}{2\times Strike}=\frac{\$1,000,000}{2\times15}=\$33,333.33VarianceNotional=2×StrikeVegaNotional​=2×15$1,000,000​=$33,333.33Realizeol(0,t)2 = 202 = 400Implieol(t,T)2 = 182 = 324t = 5T = 12PVt(T)=11+[1.50%(712)]=0.991326PV_t\left(T\right)=\frac1{1+\left[1.50\%\left({\splaystyle\frac7{12}}\right)\right]}=0.991326PVt​(T)=1+[1.50%(127​)]1​=0.991326whiis the present value interest factor after five months (i.e., scounting for seven remaining months, from t to T), where the annuinterest rate is 1.50%.Thus, the value of the swin five months is calculatefollows:Given thMonatize woullong the swap, the mark-to-market value woulpositive (i.e., a gain) for Monatize, equto $4,317,775.中文解析本题考察的是varianswap。求得是5个月后varianswap的value，比较简单，重点是记住上面的公式。需要注意的是公式中的realizevolatility，implievolatility以及strike代入数字的时候只取百分号前面的数字。另外此公式求解的是站在long position的角度的value（也就是本题中的情景）；如果题目要求的是short position的value，需要加负号。 如题

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NO.PZ201601050100001705 问题如下 Baseon the CFO’s set of assumptions, the gain on the purchase of the varianswon the S P 500 in five months woulclosest to: A.$4,317,775. B.$4,355,556. C.$4,736,334. A is correct. The gain on the varianswis calculateas:Values for the inputs are follows:Volatility strike on existing sw= 15Varianstrike on existing sw= 152 = 225Variance  Notional=Vega  Notional2×Strike=$1,000,0002×15=$33,333.33Variance\;Notional=\frac{Vega\;Notional}{2\times Strike}=\frac{\$1,000,000}{2\times15}=\$33,333.33VarianceNotional=2×StrikeVegaNotional​=2×15$1,000,000​=$33,333.33Realizeol(0,t)2 = 202 = 400Implieol(t,T)2 = 182 = 324t = 5T = 12PVt(T)=11+[1.50%(712)]=0.991326PV_t\left(T\right)=\frac1{1+\left[1.50\%\left({\splaystyle\frac7{12}}\right)\right]}=0.991326PVt​(T)=1+[1.50%(127​)]1​=0.991326whiis the present value interest factor after five months (i.e., scounting for seven remaining months, from t to T), where the annuinterest rate is 1.50%.Thus, the value of the swin five months is calculatefollows:Given thMonatize woullong the swap, the mark-to-market value woulpositive (i.e., a gain) for Monatize, equto $4,317,775.中文解析本题考察的是varianswap。求得是5个月后varianswap的value，比较简单，重点是记住上面的公式。需要注意的是公式中的realizevolatility，implievolatility以及strike代入数字的时候只取百分号前面的数字。另外此公式求解的是站在long position的角度的value（也就是本题中的情景）；如果题目要求的是short position的value，需要加负号。 只有strike price和volatility的百分号去掉吗

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