6. The current stock price of Best Business (BB) Co. is $90. The annual volatility of the stock is 40% and the risk-free force of interest is 6% per annum. In this question, we attempt to price some 1-year derivatives on BB's stock using a two-period binomial tree model. (a) Show that u and d, the multiplying factors for the up and down steps, are equal to 1.3673 and 0.7766, respectively. [2 marks] (b) Using risk-neutral pricing based on a two-period binomial tree, calculate the price of a 1-year European put option with a strike price of $95. [5 marks] An up-and-out option is one that becomes worthless if the price of the underlying ever exceeds a pre-specified barrier level. An up-and-in option is one that is worthless unless the price of the underlying ever exceeds a pre-specified barrier level; when this happens, an up-and-in option becomes an ordinary option. Suppose: Option A is a 1-year European up-and-out call option with a strike price of $95 and a barrier level of $140; Option B is a 1-year European up-and-in call option with a strike price of $95 and a barrier level of $140. (c) Using a two-period binomial tree, calculate the price of option A. [4 marks] (d) Hence, calculate the price of option B without going through another binomial tree analysis. [4 marks] [Total: 15 marks] 6. The current stock price of Best Business (BB) Co. is $90. The annual volatility of the stock is 40% and the risk-free force of interest is 6% per annum. In this question, we attempt to price some 1-year derivatives on BB's stock using a two-period binomial tree model. (a) Show that u and d, the multiplying factors for the up and down steps, are equal to 1.3673 and 0.7766, respectively. [2 marks] (b) Using risk-neutral pricing based on a two-period binomial tree, calculate the price of a 1-year European put option with a strike price of $95. [5 marks] An up-and-out option is one that becomes worthless if the price of the underlying ever exceeds a pre-specified barrier level. An up-and-in option is one that is worthless unless the price of the underlying ever exceeds a pre-specified barrier level; when this happens, an up-and-in option becomes an ordinary option. Suppose: Option A is a 1-year European up-and-out call option with a strike price of $95 and a barrier level of $140; Option B is a 1-year European up-and-in call option with a strike price of $95 and a barrier level of $140. (c) Using a two-period binomial tree, calculate the price of option A. [4 marks] (d) Hence, calculate the price of option B without going through another binomial tree analysis. [4 marks] [Total: 15 marks]
