烦请老师帮忙看下是否可以这么回答，谢谢老师

问题如下：

Calculate the value of the variance swap six months from initiation.

选项：

解释：

Correct Answer:

The value of the variance swap at time t is given by the formula:

VarSwap_t = Variance notional × PV_t (T) × {t/T × [Realized Vol(0,t)]² + [(T – t)/T)] × [ImpliedVol(t,T)]² – Strike²}

Variance notional = Vega notional / (2 × Strike) = $10,000,000/ (2 × 23) = $217,391

Realized volatility = 15² = 225

Implied volatility = 18² = 324

t = 6

T = 12

The present value interest factor after six months (discounting for six months where annual interest rate is 4.08%):

PV_t(T) = 1 / [1 + (4.08% × (6/12))] = 0.98

Var Swap = $217,391 × 0.98 × {[(6/12) × 225] + [(6/12) × 324] – 529}

= $217,391 × 0.98 × (– 254.50)

= – $54,219,565.22

Given that Nikolayev is short the variance swap, the mark-to-market value is positive for Nikolayev.

Value of the variance swap = $54,219,565