In this question, you need to price options with various approaches. You will consider puts and calls on a share.

Based on this spot price (36) and this strike price (38) as well as the fact that the risk-free interest rate is 6% per annum with continuous compounding, please undertake option valuations and answer related questions according to following instructions:

Binomial trees:

Additionally, 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%.

1. Use a two-step binomial tree to calculate the value of an eight-month European call option using the no-arbitrage approach.
2. Use a two-step binomial tree to calculate the value of an eight-month European put option using the no-arbitrage approach.
3. Show whether the put-call-parity holds for the European call and the European put prices you calculated in a. and b.
4. Use a two-step binomial tree to calculate the value of an eight-month European call option using risk-neutral valuation.
5. Use a two-step binomial tree to calculate the value of an eight-month European put option using risk-neutral valuation.
6. Verify whether the no-arbitrage approach and the risk-neutral valuation lead to the same results.
7. Use a two-step binomial tree to calculate the value of an eight-month American put option.
8. Calculate the deltas of the European put and the European call at the different nodes of the binomial three.