Problem:
Suppose there is a European at-the-money call option on a stock that expires in 3-months. The current stock price is $100 and the annual standard deviation of the stocks return is 50%. The risk free rate is 5%.
Required:
Question 1: Other than binomial options pricing, in general, what are three methods that can be used to price derivative securities?
Question 2: What is the price of the call using the binomial method with one-month steps?
Question 3: What is the value of a European at-the-money call on this stock using Black Scholes? How does it compare to part b and what explains the relationship?
Note: Please provide through step by step calculations.