Final answer:
The value of a call option is the expected payoff based on the stock's future price movement. Without the provided probabilities of the stock's price rising or falling, the exact value cannot be calculated. We know the option's value will be a fraction of the potential payoff of 6, but specific calculation requires further information.
Step-by-step explanation:
The question is about calculating the value of a call option for a non-dividend-paying stock with an expected increase or decrease in its price over a set period. To find the value of the call option, we consider two possible outcomes: if the stock price rises to 36 or falls to 26. A risk-free rate of 0 is assumed, meaning we need not discount the option's payoff.
If the stock price rises to 36, the call option will be in-the-money, and the payoff will be the difference between the stock price and the strike price, which is 36-30 = 6. If the stock price falls to 26, the call option will expire worthless, and the payoff will be 0. The value of the call option is the expected payoff, which is calculated using the probabilities of each outcome.
However, since the probabilities are not provided in the question, we cannot calculate the exact expected value. As a result, we cannot definitively select from the provided options (1.62, 2.0, 2.43, 3.0) without additional information. But we can deduce that since the option can either expire worthless or be worth 6, the value of the option has to be some fraction of 6, depending on the probabilities of the up and down movements.