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麋鹿也是鹿 · 2023年01月29日

题目条件确认

  1. CFA III
  2. Derivative

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？

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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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