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hyi725 · 2023年03月16日

如果结果为负数，说明是swap的买方要付给swap的卖方

  1. CFA III
  2. Derivative

NO.PZ2018113001000053

问题如下：

Olivia, a fund manager, sells $50,000 vega notional of a one-year variance swap on the S&P 500 at a strike of 20% (quoted as annual volatility).

If the one-year realized volatility is 18%, the settlement amount at expiration of the swap for Olivia is:

选项：

A.

pay $95,000 to the swap buyer.

B.

receive $95,000 from the swap buyer.

C.

receive $125,000 from the swap buyer.

解释：

B is correct.

Variance notional = Vega notional/(2*Strike)=50000/(2*20)=1250.

SettlementT = Variance notional × (Realized variance – Variance strike) = 1,250 × (18^2 – 20^2)

= –$95,000

If the payment amount is positive (negative), the swap seller (buyer) pays the swap buyer (seller). So, in this case, Olivia would receive $95,000 from the swap buyer.

中文解析：

本题考察的是variance swap的结算。

公式为：SettlementT = Variance notional × (Realized variance – Variance strike)

其中Variance notional = Vega notional/(2*Strike)

代入数字计算即可。

其中realized variance即σ2 ,variance strike 即X2

注意代入数字时，只取百分号前面的数字。

注意上述公式是站在long position的角度，如果结果为负数，说明是swap的买方要付给swap的卖方，本题问的是swap的卖方，因此seller是收到95,000

不懂为什么如果结果为负数，说明是swap的买方要付给swap的卖方

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已采纳答案

Hertz_品职助教 · 2023年03月16日

嗨，努力学习的PZer你好：


同学你好

这是因为题目中用于求settlement金额的那个公式是站在long position的角度来计算的。

因为结算金额，可以求long position一方的金额，取相反数就是short position的金额，因此不论是站在long还是short的一端，金额的绝对值都是一样的，相差的就是一个正负号。

而一般我们都是站在long position的角度给计算公式，可以回想下咱们在二级衍生中求衍生品的value的时候，也都是站在long position的角度来计算的，如果最后问的是short position就加负号就可以了。

 

因此站在long position的角度，计算结果是-95000，意思是long方会收到负的95000，收到负数，相当于支付95000给short一方啦。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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NO.PZ2018113001000053问题如下 Olivia funmanager, sells $50,000 vega notionof a one-yevarianswon the S P 500 a strike of 20% (quoteannuvolatility).If the one-yerealizevolatility is 18%, the settlement amount expiration of the swfor Olivia is:A.p$95,000 to the swbuyer.receive $95,000 from the swbuyer.receive $125,000 from the swbuyer. B is correct.Variannotion= Vega notional/(2*Strike)=50000/(2*20)=1250.SettlementT = Variannotion× (Realizevarian– Varianstrike) = 1,250 × (18^2 – 20^2)= –$95,000If the payment amount is positive (negative), the swseller (buyer) pays the swbuyer (seller). So, in this case, Olivia woulreceive $95,000 from the swbuyer.中文解析本题考察的是varianswap的结算。公式为SettlementT = Variannotion× (Realizevarian– Varianstrike) 其中Variannotion= Vega notional/(2*Strike)代入数字计算即可。其中realizevariance即σ2 ,varianstrike 即X2注意代入数字时，只取百分号前面的数字。注意上述公式是站在long position的角度，如果结果为负数，说明是swap的买方要付给swap的卖方，本题问的是swap的卖方，因此seller是收到95,000 答案说varianstrike是X2，题目中说varianstrike 是20，那为什么不是直接代入20，而是20的平方

2023-11-25 13:23 1 · 回答

NO.PZ2018113001000053 问题如下 Olivia funmanager, sells $50,000 vega notionof a one-yevarianswon the S P 500 a strike of 20% (quoteannuvolatility).If the one-yerealizevolatility is 18%, the settlement amount expiration of the swfor Olivia is: A.p$95,000 to the swbuyer. receive $95,000 from the swbuyer. receive $125,000 from the swbuyer. B is correct.Variannotion= Vega notional/(2*Strike)=50000/(2*20)=1250.SettlementT = Variannotion× (Realizevarian– Varianstrike) = 1,250 × (18^2 – 20^2)= –$95,000If the payment amount is positive (negative), the swseller (buyer) pays the swbuyer (seller). So, in this case, Olivia woulreceive $95,000 from the swbuyer.中文解析本题考察的是varianswap的结算。公式为SettlementT = Variannotion× (Realizevarian– Varianstrike) 其中Variannotion= Vega notional/(2*Strike)代入数字计算即可。其中realizevariance即σ2 ,varianstrike 即X2注意代入数字时，只取百分号前面的数字。注意上述公式是站在long position的角度，如果结果为负数，说明是swap的买方要付给swap的卖方，本题问的是swap的卖方，因此seller是收到95,000 如题

2023-04-07 11:47 1 · 回答

NO.PZ2018113001000053 receive $95,000 from the swbuyer. receive $125,000 from the swbuyer. B is correct. Variannotion= Vega notional/(2*Strike)=50000/(2*20)=1250. SettlementT = Variannotion× (Realizevarian– Varianstrike) = 1,250 × (18^2 – 20^2) = –$95,000 If the payment amount is positive (negative), the swseller (buyer) pays the swbuyer (seller). So, in this case, Olivia woulreceive $95,000 from the swbuyer. 中文解析 本题考察的是varianswap的结算。 公式为SettlementT = Variannotion× (Realizevarian– Varianstrike) 其中Variannotion= Vega notional/(2*Strike) 代入数字计算即可。 其中realizevariance即σ2 ,varianstrike 即X2 注意代入数字时，只取百分号前面的数字。 注意上述公式是站在long position的角度，如果结果为负数，说明是swap的买方要付给swap的卖方，本题问的是swap的卖方，因此seller是收到95,000 这个varianswap计算合约本金的公式在哪里

2022-04-22 13:26 1 · 回答

NO.PZ2018113001000053 receive $95,000 from the swbuyer. receive $125,000 from the swbuyer. B is correct. Variannotion= Vega notional/(2*Strike)=50000/(2*20)=1250. SettlementT = Variannotion× (Realizevarian– Varianstrike) = 1,250 × (18^2 – 20^2) = –$95,000 If the payment amount is positive (negative), the swseller (buyer) pays the swbuyer (seller). So, in this case, Olivia woulreceive $95,000 from the swbuyer.Payoff公式中x的平方是不是等于strike variance？与下面分母strike price一样啊？

2021-04-26 15:41 1 · 回答