Volatility Sensitivity of Deep In-The-Money European Call Options: A Black-Scholes and Non-Central F Analysis

This study investigates the sensitivity of European call option prices to volatility under the Black-Scholes framework for deep in-the-money contracts. Using the stock quantity parameter values to compute, the results show a monotonic and convex increase in call value with volatility, with total increases of $2.33 and $1.84 for S? = 60 and S? = 70, respectively. A Fisher non-central F analysis confirms that volatility explains a statistically significant proportion of price variation, with a strong effect size after controlling for the level of the initial stock price. The findings underscore the critical role of vega for deep in-the-money options and the importance of accurate volatility estimation in high-rate environments.