The price of an insurance dividend stock is $50. The volatility is 30% and the risk-free rate (all maturities) is 4% per year with continuous compounding. The stock includes a dividend of 1% per year. Use a three-step tree to value a three years European Call option with strike price $125. Required binomial tree: a) Design a three-step tree and include the prices of the stock and the value of the option on every node. b) Calculate: Per cent % of up and down movements + Probability of up and down movements. c) Use that Put-Call parity to find the value of a European Put option. d) What are the bounds for both, European Call and Put options. Do they apply with your calculus above? e) If the premium for a European call option is $1, is there any arbitrageur opportunity? Explain the strategy and find the profit. f) Find the value for an American call option. Will it be interesting to exercise it early? When? Required Balck-Scholes-Merton method: g) Use the Black-Scholes-Merton to find the value of a European Call and a Put option with same characteristics as above. h) Proof that Put-Call parity applies with the values calculated above. i) If volatility goes down, the value of a put and a call European options, will go up or down? Why? Justify your answer.