Question: The sample tree you got has 2 steps. Current stock price is $100. Annual volatility is 20%. Now make this tree have 3 steps instead

  1. The sample tree you got has 2 steps. Current stock price is $100. Annual volatility is 20%. Now make this tree have 3 steps instead of 2. In order to keep the annual volatility the same while increasing the number of steps, the 3-step tree should have upward movement as u=eT/N , where e is exponential, is annual volatility, T is time to maturity, and N is number of steps. The downward movement should be d=e-T/N .

Calculate the price of call option with a strike price of $95 using your 3-step tree. Risk-free rate is 3% and the option has 1 year to maturity.

  1. Create a binomial tree with 4 steps. Other conditions are the same as 1. What is the price of call option with a strike price of $95?

  1. How does the option price change by number of steps? Draw a graph to show the pattern. The x-axis of the graph should be number of steps and the y-axis of the graph should be the call option price. The format (not the actual value) is something like this:

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