Does the Volatility of the Underlying Asset Have a Significant Impact on the Price of a Deep ITM Option?

No, the volatility of the underlying asset has a minimal impact on the price of a deep ITM option. Since the option's Delta is near 1.0, its price is primarily driven by its intrinsic value.

The Vega (sensitivity to volatility) of a deep ITM option is very low, meaning its extrinsic value component is small and changes in volatility do not significantly affect the total premium.