Refer to the attachment.
The table below shows the closing prices (represented by letters) on a particular day for a series of European call options with different strike prices and expiry dates on a particular risky non-dividend-paying security. Call option prices Strike price 125 150 3 months W Y 6 months X Z (i) Write down, with reasons, the strictest inequalities that can be deduced for the relative values of W. X, Y,Z , assuming that the market is arbitrage-free. (Your inequalities should not involve any other quantities.) [4] Write down numerical values for a lower and an upper bound for X , given that the current share price is 120 and the continuously-compounded annual risk-free interest rate is 6%. (2] [Total 6]An investment bank has issued a special derivative security which provides a payoff in one year of: S - (50-15) if So-15 5 5, 5 50-5 10 if So-555 55+5 (So +15)-S, if So +5$5, $50+15 otherwise where S, is the price of the underlying share at time r. An investor purchases one of these special derivatives on a share with initial price $50. (i) Write down the investor's payoff from this special derivative in one year's time. [1] (ii) Explain how this payoff can be written in terms of two long and two short call options with different strike prices. [4] (ili) Calculate the fair price for this special derivative by the investor, using the following basis: volatility of the share price, 0 = 15% pa risk-free interest rate, r= 3% pa (continuously-compounded) no dividends are paid on the underlying share [5] [Total 10]The movement of a share price over the next two months is to be modelled using a two-period recombining binomial model. Over each month, it is assumed that the share price will either increase or decrease by 1 0%. (1) Over each month, the risk-neutral probability of an up-step is q =0.55. Calculate the monthly risk-free force of interest r that has been used to arrive at this figure. [1] (ii) The current share price is 1. The annualised expected force of return on the share is / =30%. Calculate the state-price deflators in each of the three possible final states of the share price. [4] (iii) Calculate the value of each of the following two-month derivatives: (a) a derivative with payoff profile (1,0,0) (b) a derivative with payoff profile (0,1,0) (c) a derivative with payoff profile (0,0,1) (P) a European call option with a strike price of K =0.95 (e) a European put option with a strike price of K = 1.05 a derivative whose payoff is 2x|5-0.98) , where S is the share price at the end of the two months. [5] A payoff profile of (x. y,=) means that the derivative returns x if the share price goes up twice, y if the share price goes up once and down once, and z if the share price goes down twice. [Total 10]An employee drew the following benefits in the month of October 2014: Basic salary Kshs, 40,000. House allowance Kshs. 30,000. Medical allowance Kshs. 16.000, Car allowance Kshs. 17.000, Entertainment allowance Kshs. 11,000 and responsibility allowance of Kshs. 14,400. During the month the employer made the following payments: Kshs.860 to NHIF, 10% of basic salary to a registered pension scheme, 6 the basic salary to the cooperative for shares and Kshs. 24,000 to a medical chemist for the drags he had taken. In addition an employee received a tax relief Ksha. 2,112. Using the tax schedule below calculate the employee's a) Gross income b) Taxable pay c) Tax charged d) The net income. Tax schedule Income (Ksh.) p.m Tax rate (% ) 1--10.800 10% 10.801--21,600 15% 21,601--32.400 20% 32.401--43,200 256 43.201 and above 30%
