The Exercise Price On A Call Option Is $30 And The Price Of

The exercise price on a call option is $30 and the price of the underlying stock is $35. The option will expire in 35 days. The option is currently selling for $5.75. a. Calculate the option's exercise value? b. Calculate the value of the premium over and above the exercise value?

The exercise price on a call option is $30, and the underlying stock currently trades at $35. The option's current market price is $5.75, and it will expire in 35 days. To analyze this option, we first determine its exercise value, which reflects the intrinsic value or the worth if exercised immediately. The exercise value of a call option is calculated as the difference between the stock price and the strike price, provided this difference is positive. In this case, since the stock price ($35) exceeds the exercise price ($30), the exercise value is $5.00 ($35 - $30). This means that if the option were exercised immediately, the holder would realize a profit of $5.00 per share.

The premium of the option ($5.75) includes both its intrinsic value and time value. The time value accounts for the potential increase in stock price before expiration and other factors such as volatility and interest rates. To find the value of the premium over the exercise value, we subtract the exercise value from the current market price. This calculation yields $0.75 ($5.75 - $5.00), which represents the additional amount investors are willing to pay for the potential future gains and flexibility that the option provides.

Investors are willing to pay more than the intrinsic value because options inherently possess extrinsic or time value. This extra value compensates for the probability that the stock price might increase further before expiration, thereby increasing the potential profit from exercising the option. Additionally, the time remaining until expiration provides the holder with the opportunity to react to market movements, hedge their positions, or take advantage of volatility, all of which add to the option's market value beyond its intrinsic worth.

Regarding the moneyness of the option, since the stock price ($35) is above the exercise price ($30), this call option is classified as "in-the-money." An in-the-money option has positive intrinsic value, making it valuable if exercised immediately. This status increases the likelihood that the option will be exercised, especially as the expiration date approaches, and often correlates with a higher premium in the market compared to at-the-money or out-of-the-money options.

If the underlying stock price decreases to $30 at expiration, the value of the option would decline to zero because the exercise value would be zero — the stock price would equal the strike price, leaving no immediate profit from exercising. Since the premium paid was $5.75, the holder would incur a loss equal to the entire premium if they chose to buy and hold until expiration and the stock price drops to $30. This illustrates the importance of stock price movements relative to the strike price in determining the option's value at expiration.

This scenario exemplifies an uncovered or naked call option, because the writer of the call does not hold the underlying shares at the outset. The writer's potential for loss is theoretically unlimited if the stock price rises above the exercise price. If the writer owned the underlying stock, it would constitute a covered call, which limits the risk. In this case, since no such protection is mentioned, it is reasonable to infer that the option is a naked call, exposing the writer to significant risk but offering potential income through premiums received.