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
-$5,500,000.000
$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.
我记得Vega Notional的含义是volatility变动1%的payoff。那么为什么不可以用Vega notional直接乘以volatility的变动求swap的value?即 PV{2,000,000 x [(16%/2 + 18%/2) - 20%]}