When european stock options have very little time until expiration (less than 2-3 hours), they can exhibit extreme sensitivity to changes in the underlying asset's price. This behavior leads to extremely high volatility values and potentially absurd Greek values.
This phenomenon occurs because option pricing models (like the Black-Scholes model) assume certain conditions, including constant volatility over the option's lifespan. As the time to expiration decreases, the option's sensitivity to changes in the underlying asset's price becomes exaggerated.
In this case, what should be the approach for volatility and greeks calculations?