Impact of Implied Volatility on Call Option Prices

A trainee analyst at a hedge fund is evaluating a European call option on a stock using the Black-Scholes Model. The stock is currently trading at $50, and the option has a strike price of $45, with 6 months until expiration. The risk-free interest rate is 2% per annum and the stock's volatility is estimated to be 30%.

The analyst calculates the option's delta, gamma, vega, and theta in an effort to understand the option's sensitivity to various parameters. However, while reviewing the formula for the Black-Scholes Model, they are uncertain about the implications of implied volatility and how it differs from the stock's historical volatility.

The analyst is faced with the challenge of comparing two European call options: one with a lower implied volatility than the stock's historical volatility and another with a higher implied volatility. They need to determine which option is likely to yield a better payoff based on changes in volatility.