Problem B2: Binomial Trees [27 marks]

A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 13% or down by 12%. The risk-free interest rate is 6% per annum with continuous compounding.

1. Use a two-step binomial tree model in the risk-neutral valuation approach to calculate the value of a six-month European put option with a strike price of $52. [6 marks]
2. Use a two-step binomial tree model in the risk-neutral valuation approach to calculate the value of a six-month American put option with a strike price of $52. [6 marks]
3. Use a two-step binomial tree model in the no-arbitrage argument valuation approach to calculate the value of a six-month European call option with a strike price of $52. [6 marks]
4. Without calculations, show the value of a six-month American call option with a strike price of 52. Explain how you come with this answer. [4 marks]
5. Show whether the put-call-parity holds for the European put and the European call. [2 marks]
6. Calculate the deltas of the European put and the European call at the different nodes of the binomial tree. Hint: You need to calculate three deltas for the call and three deltas for the put. [3 marks]