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11. The following questions are related to binomial tree option pricing. [Total: 25] Information about the underlying asset: spot price 100, expected return 15%, volatility 20%. Information about the market: risk-free rate 5.00%. (a) Consider a Cox-Ross-Rubinstein (CRR) binomial tree, in which one time step is 4 months. Calculate the up-factor u, down-factor d, and show how to get the probability (of price moving up) p. [5] (b) Consider an at-the-money American put option maturing in 1 year. Build a 3-step CRR binomial tree (i.e. show the price changes). [6] (c) Calculate the option price using the tree in question (b) and show the early exercise points if there is any. [9] (d) The price calculated in question (c) is not accurate. Explain why and how to fix this issue. [5] 11. The following questions are related to binomial tree option pricing. [Total: 25] Information about the underlying asset: spot price 100, expected return 15%, volatility 20%. Information about the market: risk-free rate 5.00%. (a) Consider a Cox-Ross-Rubinstein (CRR) binomial tree, in which one time step is 4 months. Calculate the up-factor u, down-factor d, and show how to get the probability (of price moving up) p. [5] (b) Consider an at-the-money American put option maturing in 1 year. Build a 3-step CRR binomial tree (i.e. show the price changes). [6] (c) Calculate the option price using the tree in question (b) and show the early exercise points if there is any. [9] (d) The price calculated in question (c) is not accurate. Explain why and how to fix this issue. [5]