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).
Now six months have passed, and the S&P 500 has experienced a realized volatility of 16% (annualized). On the same day, the fair strike of a new six-month variance swap on the S&P 500 is 19%.
The the current value of the variance swap sold by Olivia (note that the annual interest rate is 2.5%) is:
选项：
A.$112,963
B.$ 998,653
C.$ 159,228
解释：
A is correct.
Volatility strike on existing swap = 20.
Variance strike on existing swap = 20^2 = 400.
Variance notional = Vega notional/(2*Strike)=50000/(2*20)=1250.
RealizedVol(0,6)^2 = 16^2 = 256.
ImpliedVol(6,12)^2 = 19^2 = 361.
PVt(T) = 1/[1 + (2.5% × 6/12)] = 0.987654
The current value of the swap is
VarSwapt = 1,250 × (0.987654) × [(6/12) × 256 + (6/12) × 361 – 400]
= –$112,962.9263.
Given that Olivia is short the variance swap, the mark-to-market value is positive for her, and it equals $112,963.
为什么 the fair strike of a new six-month variance swap on the S&P 500 被用作 Implied Vol？谢谢
