I am comparing Monte Carlo estimates of VaR (using importance sampling) under both the normal and student distributions. I am also considering risk factors other than log-prices; in particular, implied volatility.
To undertake simulation one must know the sensitivities of the option price with respect to changes in the underlying risk factor. My problem is when I consider an S&P500 option and a NASDAQ option (using the current closing price and implied volatilities of the respective indexes) I get extremely large values.
From my matlab code, the parameters into BS are given below:
[p1 t1 d1 g1 v1 r1]= call_fn(2035.73 , 2050 , 0.002 , 0.1914 , 20/365); %S&P500 VIX = 19.14
[p2 t2 d2 g2 v2 r2]= call_fn(4877.49 , 5100 , 0.002 , 0.2161 , 20/365); %NASDAQ VXN = 21.61%
The outputted values of vega are 188.48 and 316.197 (SP and NAS, resp.).
These seem extremely large to me and have led me to think the numbers need modifying e.g. /365 or /100 etc. Note: I have double and triple checked that the formulas I use to compute vega are correct.