The paper titled, “Liquidity considerations in estimating implied volatility”, by Susan Thomas and Rohini Grover, is about a new way of constructing volatility index that is based on weighing the implied volatility of the options based on the relative spreads at various strikes. The key idea behind the paper is that there is considerable liquidity asymmetry across various strikes for the near month and mid month contracts on NIFTY options. This leads the authors to hypothesize a measure that is based on weighing implied volatilities. The other indices discussed in the paper are VXO, VVIX and EVIX. The obvious question is,” How should these indices be evaluated, given that the volatility is unobserved”?

The authors use 10 min squared returns to compute the daily realized volatility and use it as yard stick for comparing the VXO, VVIX, EVIX and the hypothesized SVIX(spread weighted VIX). How’s the performance of these estimators measured ?

  1. Realized volatility is regressed with each of volatility index and regression output is analyzed. Results show that adjusted R squared for VXO is slightly higher than SVIX but the difference is not sufficiently high.

  2. Instrumental variable regression where a two stage least squares is performed. Lagged IV is used an instrument variable. The results are not different from OLS regressions.

  3. Model Confidence Set Approach: There are three candidate models considered. The iterative nature of MCS shows that SVIX stands out as superior model.

Based on the above performance measures, the authors conclude that there is a case for SVIX as a better volatility index as compared to VXO, VVIX and EVIX.

Some of the questions that come to my mind as I finish reading this paper are:

  • Is the 10 min sampling frequency (used to compute realized volatility estimate) good enough that it removes incoherent microstructure noise that creates a bias in squared returns?

  • Why not consider tick time for computing RV? May be a grid search over k tick aggregated returns might give a better RV estimate. This RV estimate can be used as a yard stick for measuring the performance.

  • The paper compares just three models. Somehow I have always thought MCS approach is useful when there are a large set of competing models. With just three models, the probability of the two pruned out models reported in the paper are 0.019 and hence by the very design of MCS framework, the probability that is assigned to SVIX model is 1. The question I have in mind is that, “Does MCS framework has adequate power when you use it for three models?”

  • In a simulation study by PR Hansen, one of the conclusions is this : MCS yields a set of models that contains all, or almost all, truly superior models, but rarely exactly captures the “true” set of superior models, unless the difference in expected performance of superior and inferior models is large. This effect is far more pronounced when one uses few models for MCS procedure.

Someday I will get to figuring out the answers for the above questions.

One thing I must say is this: I found the paper extremely well written in terms of the logical sequence of arguments used for making a case for SVIX.