Final answer:
The price of the one-year put option on Estelle stock using the Binomial Model is $4.25.
Step-by-step explanation:
To calculate the price of a one-year put option on Estelle stock using the Binomial Model, we need to consider the possible stock price movements over the next two years. In each year, the stock price will either go up by 23% or go down by 23%. The current price of the stock is $20.00.
Step 1: Calculate the potential future stock prices after year 1. The stock price can either be $20.00 * (1 + 0.23) = $24.60 or $20.00 * (1 - 0.23) = $15.40.
Step 2: Calculate the potential future stock prices after year 2. If the stock price goes up in year 1 to $24.60, it can either go up in year 2 to $24.60 * (1 + 0.23) = $30.26 or go down to $24.60 * (1 - 0.23) = $18.94. If the stock price goes down in year 1 to $15.40, it can either go up in year 2 to $15.40 * (1 + 0.23) = $18.92 or go down to $15.40 * (1 - 0.23) = $11.87.
Step 3: Calculate the payoffs for each potential future stock price at the end of year 2. If the stock price is $30.26, the payoff is $0 as the stock price is above the strike price of $20.00. If the stock price is $18.94, the payoff is $20.00 - $18.94 = $1.06. If the stock price is $18.92, the payoff is $20.00 - $18.92 = $1.08. If the stock price is $11.87, the payoff is $20.00 - $11.87 = $8.13.
Step 4: Discount the payoffs back to year 0 using the risk-free interest rate of 6.9%. The present value of each payoff is calculated as the payoff divided by (1 + risk-free interest rate)^(number of years to expiration). The present value of the $1.06 payoff is $1.06 / (1 + 0.069)^2 = $0.94. The present value of the $1.08 payoff is $1.08 / (1 + 0.069)^2 = $0.95. The present value of the $8.13 payoff is $8.13 / (1 + 0.069)^2 = $7.21.
Step 5: Calculate the expected present value of the payoffs by multiplying each payoff's present value by their respective probabilities. The probability of reaching each potential future stock price is 0.5. Therefore, the expected present value of the payoffs is (0.5 * $0.94) + (0.5 * $0.95) + (0.5 * $7.21) = $4.53.
Step 6: Discount the expected present value of the payoffs back to year 0 to get the price of the put option. The price of the put option is $4.53 / (1 + 0.069) = $4.25.