NO.PZ201601050100001705
问题如下:
Based on the CFO’s set of assumptions, the gain on the purchase of the variance
swap on the S&P 500 in five months would be closest to:
选项:
A.$4,317,775.
$4,355,556.
$4,736,334.
解释:
A is correct.
The gain on the variance swap is calculated as:
Values for the inputs are as follows:
Volatility strike on existing swap = 15
Variance strike on existing swap = 152 = 225
RealizedVol(0,t)2 = 202 = 400
ImpliedVol(t,T)
2 = 182 = 324
t = 5
T = 12
which is the present value interest factor
after five months (i.e., discounting for seven remaining months, from t to T), where
the annual interest rate is 1.50%.
Thus, the value of the swap in five months is calculated as follows:
Given that Monatize would be long the swap, the mark-to-market value would be
positive (i.e., a gain) for Monatize, equal to $4,317,775.
中文解析:
本题考察的是variance swap。
求得是5个月后variance swap的value,比较简单,重点是记住上面的公式。
需要注意的是:
公式中的realized volatility,implied volatility以及strike代入数字的时候只取百分号前面的数字。
另外此公式求解的是站在long position的角度的value(也就是本题中的情景);如果题目要求的是short position的value,需要加负号。
over the next 5 month, volatility is 20%,所以默认现在是时间点0开始在7个月吗?
老师可以画图一下吗
没明白为什么公式里减去X的平方是15的平方而不是减去18的平方
新的strike price不是18吗?