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ica.kiwi · 2024年07月23日

如果说5个月过去了，那么t和T的关系是什么样子的呢？这里我容易混淆。

  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.

如题。

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1 个答案

pzqa27 · 2024年07月23日

嗨，努力学习的PZer你好：


 那就用下面这个式子

$50,000 × (0.990099) × [(5/12) × 256 + (7/12) × 324 – 400]


先用5个月已经实现的波动率+7个月预期的波动率-约定的执行波动率

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

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