I am testing a local volatility pricer by comparing its results under two settings:
- Pricing a 5yr ATM call option with a flat volatility of $0.194$
- Pricing the call option with the typically shaped equity vol surface: in particular, the minimum implied vol figure is $0.195$ (longest maturity / ATM strike) and the maximum implied vol is $0.245$ (shortest maturity / lowest strike)
By intuition, using a implied vol surface where all the individual volatility points are above $0.194$ should deliver a higher call price than using a flat volatility. However, the local vol pricer that I am testing (black-box) delivers lower option values when the input is the [$0.194$ to $0.245$] vol surface than when I use a single $0.194$ flat figure.
Is that enough evidence to conclude that the local vol implementation is flawed? Or should I distrust my intuition?