1. A large national employer currently provides a defined benefit pension scheme for its

workforce. It has been decided that a new defined contribution scheme will be set up

for new employees. The new scheme will aim to provide a significant degree of

flexibility for its members. For example at retirement members will not be required

to purchase an annuity.

(i) Set out the advantages for the employer of setting up a defined contribution

scheme for new employees rather than continuing to use the existing defined

benefit scheme. [4]

(ii) Set out the key aspects of scheme design that could be considered by the

employer to incorporate the desired flexibility in the new scheme. [6]

(iii) Outline the issues that individual members in the new defined contribution

scheme need to consider as they are approaching retirement. [5]

(iv) Discuss the advantages and risks to the member of taking income drawdown

rather than purchasing an annuity at retirement. [8]

2.(i) List six options for the provision of the outstanding benefit payments that may

exist if a defined benefit pension scheme is being discontinued. [3]

(ii) Discuss the key features of each option in part (i). [6]

(iii) Comment on the circumstances in which each of the options in part (i) might

be most appropriate. [3]

3.

A company has issued zero-coupon bonds payable in ve years' time for a nominal amount oflm, The company has also issued 1 million non-dividendpaying shares. A Black-Scholes model for the value of the company is adopted. (i) Derive an expression for the value of the debt at time {i using the Merton model, in terms of the total value of the company and the value of a call option. [4] The current total value of the company is 20{}m. The continuously compounded risk-free interest rate is 1% per annum. The current arbitragefree prices of options on the company's shares, with maturity in ve years\" time and a strike price of l, are as follows: I put option = 1130 I call option = 2155 (ii) Calculate, using put-call parity, the value of the zero-coupon bonds per 101} nominal, [3] The volatility of the total value of the company is 17% per annum. (iii) Determine the approximate change in the share price and the bond price that would arise from a film increase in the total value of the company. [Hint: consider the delta of an appropriate option] [4] {iv} Comment on the relative change in the share and bond prices in part (iii), [2] {v} Comment, without carrying out any calculations, on how the relative change in part (iii) would differ if the total value of the company was lower, [1] Andy is playing a game, which involves rolling four-sided fair dice. Each time a dice is rolled, it is equally likely to show one of the numbers: 1, 2, 3 or 4. Before each roll, he has three strategies: a: Receive 1.5 times the number showing. a,: Receive half the number showing if it is odd, and twice the number if it is even. a3: Receive the number showing if it is even, and twice the number if it is odd. Construct Andy's payoff matrix. [2] State which, if any, of the decision functions are dominated. [1] (iii) Determine Andy's optimal strategy under the Bayes criterion. [3]