Final answer:
To calculate the value of the put option, one would use a simplified binomial model, considering the stock's potential rise to $42 or fall to $37 against the option's strike price of $41 and adjusting for the 1% risk-free rate. The option's payoff would be $4 if the stock price falls to $37, and $0 if it rises to $42. Actual calculation requires probabilities of stock movement, which are not given.
Step-by-step explanation:
To calculate the value of the put option for a non-dividend-paying stock, we can use a simplified version of the binomial option pricing model. With the current price of the stock at $40 and the expected rise to $42 or a fall to $37 over the next year, and a put option strike price of $41, we can calculate the potential values of exercising the option in both scenarios.If the stock price falls to $37, the value of the put option at expiration would be the strike price minus the stock price, which is $41 - $37 = $4. If the stock price rises to $42, the option would expire worthless as there would be no point in exercising the option to sell at $41 when the market price is higher at $42. The present value of the option's payout must also be adjusted by the risk-free interest rate, which is 1% in this example.
To find the expected value of the option, we'll use the two possible outcomes ($4 or $0), and adjust for the probability of each outcome and the time value of money: Value if stock price falls: $4 / (1 + risk-free rate)
Value if stock price rises: $0 The actual calculation would require more information about the probabilities of the stock's movements, which is not provided, so we cannot give a specific numeric answer.