A firm of financiers has previously operated as a partnership. The firm is considering

raising a large loan in order to buy office premises instead of renting them. One of

the partners has suggested incorporating the firm as a limited company in order to

avoid personal risk for the partners at minimal cost.

Explain whether incorporation as a limited company is likely to achieve the objectives

suggested by the partner.

[5]

The directors of a major quoted company are considering raising funds by means of a

rights issue.

Describe the matters that will have to be decided by the directors if they decide to

proceed with the issue.

[5]

An investor purchased convertible loan stock in a small company. The exercise

period for converting the stock into equity is two years in the future. However, the

company has written to the investor offering to permit the conversion to go ahead

immediately and on slightly more favourable terms than had been originally offered.

Describe the factors that should be taken into account by the investor in deciding

whether to accept this offer.

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(i) Write down an expression for the price of a derivative in a Black-Scholes market in terms of an expectation under the risk-neutral measure, defining any additional notation that you use. [3] Consider an option on a non-dividend-paying stock when the stock price is $50, the exercise price is f49, the continuously compounded risk-free rate of interest is 5% per annum, the volatility is 25% per annum, and the time to maturity is six months. (ii) Calculate the price of the option using the Black-Scholes formula, if the option is a European call. [4] (iii) Determine the price of the option if it is an American call. [1] (iv) Calculate the price of the option if it is a European put. [2] (v) Determine how the prices of the contracts in parts (ii) to (iv) would change in the case of a dividend-paying underlying stock. [Note that you do not have to perform any further calculations.](i) State the main potential drawback of the Vasicek model. [1] (ii) Discuss the extent to which this drawback may be a problem. (3] (iii) Explain how the Cox-Ingersoll-Ross model avoids this drawback. [3] The Vasicek term structure model is described by the following stochastic differential equation: dr, = a(b-r, )di + odw,, and a, b, 6 >0. Under this model, the short rate r, follows a Normal distribution with mean E(r,) = ne "+b(1-e-") and variance Var (r, ) = --(1-e-2ar ). (iv) Assess, using the information provided above, whether the model generates interest rates that are mean reverting and, if so, the value to which they revert. [2] (v) Assess, using the information provided above, the relevance of the parameter a to any mean reversion. [21(i) Explain what is meant by a conjugate prior distribution. [1] The random variables X1, X2, ..., X,, are independent and have density function: P(X = x)= p(1-p)',0