Deep OTM implied Variance Can Never Rise

Market participants commonly extrapolate the implied volatility skew for far out of the money strikes with a flat asymptote. We show that if it were possible to trade in a frictionless way options priced according to this... [ view full abstract ]

Market participants commonly extrapolate the implied volatility skew for far out of the money strikes with a flat asymptote. We show that if it were possible to trade in a frictionless way options priced according to this assumption, the asymptotical level of the corresponding implied variance (square of the implied volatility times the residual maturity) could never rise. It echoes the result of Dybvig-Ingersoll-Ross on the long term interest rates that can never fall, although the condition is on the strikes, not on the maturities. Actually the long term variance swap rate can fall or rise with no restriction.