hey tutors these are the questions in images i need solving

a)

A defined benefit pension scheme ("the Scheme") provides a non-escalating pension at a specific retirement age, together with a contingent spouse's pension equal to a fixed percentage of the pension payable to the member. The Scheme is set up under trust and the trustees have decided that greater choice should be offered to members when they reach retirement age. (i) List the options that the trustees might consider offering to members, assuming that there are no legislative constraints. [5] The trustees have decided that members should be offered a transfer value at retirement, as an alternative to the pension payable under the Scheme. The transfer value would have to be used to purchase a lifetime annuity with an insurance company. (ii) Outline the issues that a member should consider when deciding whether to accept this option. [5]A share is currently priced at 640p. A writer of 100,000 units of a one year European put option with an exercise price of 630p has delta-hedged the option with a portfolio which holds cash and is short 24,830 shares. The continuously compounded risk-free rate of interest is 3% p.a. and no dividends are payable during the life of the option. The assumptions of the Black-Scholes model apply. (i) (a) Write down an expression for the delta of the option. (b ) Calculate its value in this case. [4] (ii) Prove that the volatility of the share implied by the delta is 7.1% p.a. (assuming it is less than 100%). [5] (iii) (a) Calculate the price of the option. (b) Determine the value of the cash holding in the hedging portfolio. [4] [Total 13](i) (a) Explain why an insurance company might purchase reinsurance. (b) Describe two types of reinsurance. [3] The claim amounts on a particular type of insurance policy follow a Pareto distribution with mean 270 and standard deviation 340. (ii) Determine the lowest retention amount such that under excess of loss reinsurance the probability of a claim involving the reinsurer is 5%. [4] [Total 7]Why might a company choose to attach a warrant to a bond issue? A Bondholders might accept a lower rate of interest in the expectation of a capital gain. B Bondholders are attracted by the additional protection offered by a warrant. C Warrants reduce the tax payable by the company. D Warrants dilute shareholder returns. [2]