1. An investor is planning to model the price, St at time t, of a non-dividend paying share using a l-period trinomial tree, in which share price at time 1, S1, can either be: u So with risk-neutral probability qui So with risk-neutral probability Im; or d So with risk-neutral probability qa; where u >1>d and 9, +4m + 40 = 1. The constant continuously compounded risk-free rate of interest per unit of time is r. (a) Using no-arbitrage arguments, show that: uqu +9m +d4. = e". [3 marks (b) Determine the current prices of the following derivatives maturing at time 1: (i) A European call option contract on the share with strike price So. [2 marks (ii) A European put option contract on the share with strike price So. [2 marks] (c) Show that the prices obtained in part (b) satisfy the put-call parity. (4 marks] (d) Discuss the main shortcoming of the arbitrage-free price obtained using the above trino- mial tree model. [3 marks] (Total: 14 marks] 1. An investor is planning to model the price, St at time t, of a non-dividend paying share using a l-period trinomial tree, in which share price at time 1, S1, can either be: u So with risk-neutral probability qui So with risk-neutral probability Im; or d So with risk-neutral probability qa; where u >1>d and 9, +4m + 40 = 1. The constant continuously compounded risk-free rate of interest per unit of time is r. (a) Using no-arbitrage arguments, show that: uqu +9m +d4. = e". [3 marks (b) Determine the current prices of the following derivatives maturing at time 1: (i) A European call option contract on the share with strike price So. [2 marks (ii) A European put option contract on the share with strike price So. [2 marks] (c) Show that the prices obtained in part (b) satisfy the put-call parity. (4 marks] (d) Discuss the main shortcoming of the arbitrage-free price obtained using the above trino- mial tree model. [3 marks] (Total: 14 marks]