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Do you think that the negative sign of volatility risk premium that many articles suggest like Bakshi and Kapadia (2003) is reasonable? Any other articles that i should read? I have found an article of Liu and Pan (2003) that assumes negative volatility risk premium in order to solve the problem of asset allocation. do you know any empirical research on this article or a similar one?

There's nothing inherently implausible about a negative volatility risk premium. However, I don't think enough is understood about stochastic volatility, or indeed implied versus actual volatility, to start pricing volatility risk. As far as I know, only a few people have picked up on this area of research, and it has yet to yield practical results. It may turn out to be productive, either in theory or in practice or both.

In my guess, negative volatility risk premium implies positivity of the covariance between the pricing kernel and the averaged integrated volatility i.e. means that expected future volatility is less than implied volatility.It could happen after a long negative shock to demand on instant t, investors are willing to give money for all investments highly exposed to volatility risk (and receive money for low volatility risk assets), in order to increase their total wealth on time t+1. Negative volatility risk premia hypothesis is real and possible. Rgds,

First of all thank you for your answers. I agree with Aaron that it is quite difficult to measure the price of risk but the article of Bakshi and Kapadia focus on the sign rather than the magnitude of the volatility risk premium. The problem is that i am not very convienced about their methodology. the main idea is that a portfolio that is delta neutral should have zero excess returns. even if this approach do not have problems (they argue that using B-S delta hedge ratio is not wrong), they find out that the "delta- hedged" losses are 0.07% (2003a) for the index options and 0,03%(2003b) for the equity options. do you think that those numbers are big enough to justify the use of Heston instead of another model that does not take into account volatility risk premium? heston's model may be more accurate but i do not think that such a small number justify its use (and all the problems that has for the calculations of its parameters).

Although the absolute returns appear low, remember that they are flows based on the notional amount. They are much larger as a percentage of option premium. As I recall (it has been many years since I read the paper) the effect was on the order of 20% for out-of-the-money options.Another explanation is that actual volatility was lower than expected over the period. The authors demonstrate that is statistically implausible. However there are many financial variables that appear to be systematically under (or over) estimated by simple models.I think this is an interesting idea, but it will need a lot more work to gain widespread acceptance.