Lower Bound Calculation for European Call Option with Strike Price of 25 and 219 Days to Expiration

Explanation

To determine the lower bound on the value of the European call option, we can use the concept of intrinsic value. The intrinsic value of a call option is the maximum of zero and the difference between the underlying asset's price and the strike price.

In this case, the strike price of the option is $25, and the underlying stock is currently trading at $29. Therefore, the intrinsic value of the option is the maximum of zero and ($29 - $25), which is $4.

However, since the option has 219 days until expiration and the analyst believes that the stock will be valued at $35 by the expiration date, there is a possibility of additional value for the option due to the potential price increase. This potential additional value is known as the time value of the option.

To calculate the time value of the option, we need to use an option pricing model, such as the Black-Scholes model. This model takes into account factors such as the time to expiration, the volatility of the underlying asset, the risk-free rate, and the strike price.

Since the question provides the risk-free rate of 4.0%, we can use this rate in the option pricing model. However, the question does not provide the volatility of the underlying asset, which is required for an accurate calculation of the time value. Without the volatility, we cannot determine the exact time value or the upper bound on the value of the option.

Based on the given information and the absence of volatility, we can conclude that the lower bound on the value of the option is its intrinsic value, which is $4. Therefore, the correct answer is option B: $4.00.