In this question, you need to price options with binomial trees. You will consider puts and calls on a share with spot price of $30. Strike price is $34. Furthermore, assume that over each of the next two four-month periods, the share price is expected to go up by 11% or down by 10%. The risk-free interest rate is 6% per annum with continuous compounding.

a. Use a two-step binomial tree to calculate the value of an eight-month European call option using the no-arbitrage approach.

b. Use a two-step binomial tree to calculate the value of an eight-month European put option using the no-arbitrage approach.

c. Show whether the put-call-parity holds for the European call and the European put prices you calculated in a. and b.

d. Use a two step-binomial tree to calculate the value of an eight-month European call option using risk-neutral valuation.

] e. Use a two step-binomial tree to calculate the value of an eight-month European put option using risk-neutral valuation.

] f. Verify whether the no-arbitrage approach and the risk-neutral valuation lead to the same results.

g. Use a two-step binomial tree to calculate the value of an eight-month American put option

h. Without calculations: What is the value of an eight-month American call option with a strike price of $34? Why?

i. Without calculations: Consider an at-the-money European put on the same share and a timeto-maturity of 8 months. Will the price of the at-the-money put be higher or lower compared to the put price you calculated in e.? Why?

j. Without calculations: What would happen to the option prices you calculated in d. and e. if the interest rate drops to 4%?