working solns!! don't copy

a)Agency theory identifies certain types of cost as agency costs.

I Directors salaries

II Directors bonuses

III The auditor s fee

IV Employees pay rises

b)

(i) State the main assumptions underpinning the Black-Scholes model. [3] Consider a put option on a non-dividend paying stock when the stock price is $8, the exercise price is $9, the continuously compounded risk-free rate of interest is 2% per annum, the volatility is 20% per annum. and the time to maturity is three months. (ii) Calculate the price of the option using the Black-Scholes model. [4] (iii) Discuss how the price of the contract in part (ii) would change if the rate of interest increases. (There is no need to carry out further calculations.) (2]A Markov jump process has the following generator matrix: -0.3 0.2 0.1 B 0.1 -0.5 0.4 C 0.3 0.1 -0.4 (i) Draw a transition graph for this process. [2] The process is in state A at time zero. (ii) Give Kolmogorov's forward equations for - P (1), " P (1) and Pic(1). [2] (iii) Calculate the probability that the process remains in state A throughout the period / = 0 to / = 2. [2] (iv) Determine the probability that the third jump of the process is into state C. [3]