Jagged Quote of IV for BlackVarianceSurface

Question

I am following this example and trying to adapt it to my needs.

In the section of code:

implied_vols[i][j] = data[j][i]

implied_vols = ql.Matrix(len(strikes), len(expiration_dates))
for i in range(implied_vols.rows()):
    for j in range(implied_vols.columns()):
        implied_vols[i][j] = data[j][i]
  [1]: http://gouthamanbalaraman.com/blog/volatility-smile-heston-model-calibration-quantlib-python.html

This assumes the IV matrix has all corresponding strikes for a given expiry. In fact, the [mass] quote is often stored in a dictionary instead of an array exactly for this reason.

For example in the SPX, we have different strike increments at different expiration. So some strikes are empty for one expiry but not another. I realize I can force the situation by making the matrix cell always have numerical value, but I am assuming that inserting a 0 at a given strike/expiry is a bad idea. Alternatively, forcing all expiry to the least common denominator of strikes between the expiry throws out lots of data.

What happens if the volatility quotes you have are not square and you don't want to throw out data when building a ql.Matrix to hand to BlackVarianceSurface?

Answer 1

Unfortunately, there's no ready-made solution. As you say filling the missing cells with 0 is a bad idea; but filling them by interpolating manually the missing values should work. The way to do it probably depends on how sparse your data is...