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麋鹿也是鹿 · 2023年01月29日

题目条件确认

NO.PZ2018113001000077

问题如下:

Marcus, who works for an investment management company, is asked to calculate what the gain would be in 6 months on a purchase of $2,000,000 vega notional of a one-year variance swap on the S&P 500 at a strike of 20% (quoted as annual volatility).

Now six months have passed, and the S&P 500 has experienced a realized volatility of 16%The fair strike of a new 6-month variance swap on the S&P 500 will be 18%.

The annual interest rate is 2.00%

The current value of the variance swap is:

选项:

A.

-$5,445,544.500

B.

-$5,500,000.000

C.

$5,445,544.500

解释:

A is correct

中文解析:

本题考察的是variance swap。

需要求解的是variance swap在6个月时刻的value:

第一步,计算variance notional = $2,000,000/(2×20)=50,000

第二步,计算折现因子PVt (T)=1/[1 + (2.00% × 6/12)] = 0.990099

第三步,直接带入公式计算,VarSwapt= $50,000 × (0.990099) × [(6/12) × 256 + (6/12) × 324 – 400]= -$5,445,544.500.

题目中说的variance swap是6个月的,那么6个月后,这个swap就到期了,此时的value不是应该等于payment么?

1 个答案
已采纳答案

Hertz_品职助教 · 2023年01月29日

嗨,努力学习的PZer你好:


同学你好

请看题干第一段后半部分哈:…on a purchase of $2,000,000 vega notional of a one-year variance swap

这个variance swap是一年期的,不是6个月期限的。求的是在6个月这个时间点的value。

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

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