Hi,

The answer lies in the relationship between the VIX index and the 30-day variance swap rate. Essentially, the squared VIX index approximates the conditional risk-neutral expectation of the annualized return variance, over the following 30 days, which is the 30-day variance swap rate.

The realized return variance can be split in different components showing that only OTM calls and puts give a contribution in its replication.

Please have a look at the attached paper (pp. 15-16), where an extensive explanation is provided.

Best regards

http://www.math.nyu.edu/research/carrp/papers/pdf/JODCarrWu.pdf