This script implements calculation of vol. of vol parameter for different maturities using formula (6) mentioned in Piterbar's paper "Time to Smile".
It uses same input data, and generates calculated values for expiry 1 to 7 years. Following is generated output after running this program:
results =
0.00000 0.75000 0.75000
1.00000 0.81000 0.80376
2.00000 0.87000 0.86260
3.00000 0.93000 0.92393
4.00000 0.99000 0.98561
5.00000 0.10500 1.04716
6.00000 0.11100 1.10816
7.00000 0.11700 1.16848
Columns in the above table are:
column 1 : expiry
column 2 : effective vol of vol values mentioned in paper
column 3 : calculated values for effcetive vol of vol