Estimate the value of the European six-month put option using the Black-Scholes model: Explain to students what happens when the number of steps in the binomial tree increases to a very large number.

 QUESTION 1 (5 + 2 + 3 + 5 = 15 marks)

You been invited to the university to do a lecture on option pricing methods (including binomial trees and the Black-Scholes model). Vinay has asked you to:

1. a)  Show students how to estimate option prices using the binomial tree model. Using a live demonstration on Bloomberg you identify the following information: 1 USD = 1.30 AUD, the volatility of the USD/AUD currency pair is 40% per annum, the US risk-free rate is 1.50% per annum with continuous compounding and the AUD risk-free rate is 1.75% per annum with continuous compounding. Using a four-step binomial tree calculate the price of a European six month put option to sell 1 USD for 1.40 AUD.
2. b)  Using the same information in part a) estimate the value of the European six-month put option using the Black-Scholes model. In addition, explain to students what happens when the number of steps in the binomial tree increases to a very large number.
3. c)  Using the same information as part a) estimate the price of an American six month put option to sell 1 USD for 1.40 AUD. In addition, explain why the American option price differs from the European option price.

16. d)  For the final part of the lecture show using Microsoft Excel how students can estimate implied volatility using option information. From Bloomberg you identify that the price of a nine- month silver futures contract is 16.50, the risk-free rate is 1.50% per annum with continuous compounding, and the dividend yield is 3.80% per annum with continuous compounding. Calculate implied volatility for the following futures options on silver with six-months to maturity and explain the importance of implied volatility.