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和棋 · 2022年04月22日

公式在哪

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

这个variance swap计算合约本金的公式在哪里
1 个答案

Hertz_品职助教 · 2022年04月22日

嗨,爱思考的PZer你好:


同学你好~

本题求的是variance swap的结算金额,即settlement amount,所以解析中第二行和第三行给到的公式以及带入的数字都是settlement 的计算公式,没有求value的公式哈。

这部分公式对应在强化班15页,我也截图放在下面,同学可以复习一下哈


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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

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