Final answer:
The value of the call option in a binomial model, when combined with 0.5 shares of stock to create a riskless portfolio, equals $2.00. This is calculated by deducting the present value of the short call option ($5.40) from the value of the 0.5 shares ($7.40).
Step-by-step explanation:
The riskless portfolio mentioned contains 0.5 shares of a stock with a combined present value of $7.40. Additionally, a short call option tied to this stock has a present value of $5.40.
To find the value of the call option, you need to create a riskless position by combining the option with the stock such that no matter how the stock price changes, the combined position's value remains the same.
To clarify, since you're holding 0.5 shares and shorting the call option, it implies that the value of the short call plus the cash should equal the value of the 0.5 shares ($7.40) to maintain a riskless position. Therefore, the value of the call option would be:
Value of 0.5 shares - Present value of short call = $7.40 - $5.40 = $2.00.
This calculation assumes a one-step binomial model where the portfolio rebalancing occurs only once.