Black-Scholes-Merton model:

please do Black-Scholes-Merton model: portions only

Problem C2: Option Valuation and Properties of Options (26 marks) In this question, you need to price options with different valuation approaches and comment on your results. You will consider puts and calls on a share with a spot price of $47.8. Strike price is $50. The risk-free interest rate is 6.14% per annum with continuous compounding. Binomial trees: Furthermore, assume that over each of the next two three-month periods, the share price is expected to go up by 8% or down by 8%. a. Draw a two-step binomial tree and populate the individual nodes with the share price values at each node. [1 marks] b. Use the two-step binomial tree from a. to calculate the value of a sixmonth European call option using the no-arbitrage approach. [3 marks] c. Use the two-step binomial tree from a. to calculate the value of a sixmonth European put option using the no-arbitrage approach. [3 marks] d. Show whether the put-call-parity holds for the European call and the European put prices you just calculated in b. and c. [2 marks] e. Use the two-step binomial tree from a. to calculate the value of a sixmonth European call option using risk-neutral valuation. [2 marks] f. Use the two-step binomial tree from a. to calculate the value of a sixmonth European put option using risk-neutral valuation. [2 marks] g. Verify whether the no-arbitrage approach and the risk-neutral valuations lead to the same results. [1 mark] h. Use the two-step binomial tree from a. to calculate the value of a sixmonth American put option. [2 marks] Notes: 1. When you use no-arbitrage arguments, you need to show in detail how to set up the riskless portfolios at the individual nodes of the binomial tree. Black-Scholes-Merton model: Furthermore, assume that the volatility of the underlying asset is 16% per annum. i. What is the Black-Scholes-Merton price of a six-month European call option? [2 marks] j. Without calculations, show the price of a six-month American call and provide an explanation for your answer. [1 mark] k. What is the Black-Scholes-Merton price of a six-month European put option? [2 marks] I. Verify whether the put-call parity holds for the option prices you just calculated in i. and k. [1 mark] m. Without calculations: What would happen to the option prices you just calculated in i. and k. if the interest rate declines to 5.5% ? Why? [2 marks] Comparison across models: n. Compare the call option prices you just calculated in e. and i. Compare also the put option prices you just calculated in f. and k. Do you expect these prices to be the same? Why/Why not? [2