Variance Risk Premium as Implied Versus Realized Variance

Summary

The document gives an intuitive definition of the variance risk premium (VRP): the difference between squared option-implied volatility and squared historical volatility. It describes research findings that S&P options have, on average, been priced with implied volatility above subsequently observed historical volatility. The comparison is expressed in variance terms, so it concerns squared volatility measures rather than their simple difference.

One proposed economic interpretation is that options provide insurance in adverse economic conditions, when volatility tends to rise. Investors may value that protection, increasing option prices and implied volatility relative to realized volatility. The explanation presents this as a likely reason for the observed premium, not as a definitive causal account. It offers no calculation procedure, sample details, or discussion of how results depend on the chosen horizon and volatility measures, so interpretation of a particular time series requires additional definitions and evidence.

Key ideas

• The variance risk premium compares squared implied volatility with squared historical volatility.
• The document reports that S&P option implied volatility has tended to exceed historical volatility on average.
• Options may be valuable as insurance because volatility often rises in difficult economic states.
• The insurance explanation is a proposed interpretation rather than a proven cause.

Tags

# What is the variance risk premium?


# What is the variance risk premium?












Can someone provide an intuitive understanding of the variance risk premium? I am very confused by this definition and cannot interpret my time series analysis.

## Answer by Alex C (score 6, accepted)

https://quant.stackexchange.com/a/21032

Intuitively: empirical research has shown that options on the S&P are priced at a slightly higher implied vol than the actual historical vol of the S&P (on average). Why? Likely this is because holding these options provides insurance against bad states of the economy (volatility increases when the economy is in trouble); this is valuable and raises their price. In any case, the difference between the squared implied vol and the squared historical vol is called the VRP or Variance Risk Premium. The key paper is Bollerslev's in RFS 2009 (cited above by Phun).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.