Final answer:
To calculate the price of an option using the binomial model, we need to consider the probability of stock price movements and the present value of future stock prices.
Step-by-step explanation:
In order to calculate the price of an option using the one-step binomial model, we need to consider the probability of the stock price moving up and down, as well as the present value of the future stock prices. Using the provided information, we can calculate the probability of the stock price moving up as follows:
Probability of moving up = (Stock price at maturity - Stock price at beginning)/(Stock price when moving up - Stock price when moving down)
Once we have the probability of moving up, we can use it to calculate the present values of the possible stock prices at the end of 6 months, and then use those probabilities to calculate the option price. For the one-step binomial model:
Option price = (Probability of stock price moving up * Present value of stock price moving up + Probability of stock price moving down * Present value of stock price moving down)/Risk-free interest rate
Using the two-step binomial model, the calculations are similar, but we would use probabilities and present values for two steps instead of one.