I am reading through Derman's 1999 research notes, "More than you ever wanted to know about Volatility Swaps."
In equation B4 of Appendix B, the author takes the Taylor Series of the variance swap replication portfolio with the constant term being equal to implied volatility squared. For me, this implies that the fair strike of a variance swap is equal to implied volatility squared when there is no skew in the IV surface.
I developed a tool to replicate fair variance strike and I always get a value higher than the IV squared when I use constant volatility to price each option in the replication. I get similar results when I use my trader's pricer at my job. I doubt there is a numerical error as I am simply doing a partial sum. Hence, I would expect the error to underprice the fair strike.
Should the fair variance price be equal to IV squared in the absence of skew and curvature in the IVS? If not, why?