The price of an "insurance dividend stock" is $75. 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 an eighteen months European Call option with strike price $62.50. Required Balck-Scholes-Merton method: a) Use the Black-Scholes-Merton to find the value of a European Call and a Put option with the same characteristics as above. b) Proof that Put-Call parity applies with the values calculated above. c) If interest rates rise, the value of a put and a call European options, will go up or down? Why? Justify your answer. Required binomial tree: d) Design a three-step tree and include the prices of the stock and the value of the option on every node. e) Calculate: Per cent % of up and down movements + Probability of up and down movements. f) Use that Put-Call parity to find the value of a European Put option. g) What are the bounds for both, European Call and Put options. Do they apply with your calculus above? h) If the premium for a European Call option is $30, is there any arbitrageur opportunity? Explain the strategy and find the profit. i) Find the value for an American call option. Will it be interesting to exercise it early? When