Discuss the effect of injections and withdrawals on the circular flow of income.

Consider an economy where the short rate of interest / follows the lognormal stochastic process: dr =u(r,t)rdt + o(r,t)rdz where z is a standard Brownian motion. In this economy, the prices of all traded assets depend only on the short rate r and its evolution over time. (1) (a) Describe the "market price of risk", 2., in the context of the stochastic process. (b ) Show (either by argument or by algebra) that ). cannot be a function of any traded asset. [5] The price of a traded asset /= 1(r, t, T) satisfies the following partial differential equation (PDE): av +r( u- 20) at or The finite difference method can be used to obtain a numerical solution to the above PDE. The binomial tree valuation method is also a widely used alternative to the finite difference method. (1i) (a) Discuss how each of these two methods achieves a solution to the PDE. (b) Comment on the relative suitability of each method for the valuation of options.An insurance company with substantial domestic pensions business is reviewing its policy with respect to derivatives across various asset classes. The actuarial risk function is concerned about the amount of longevity and Limited Price Indexation (LPI) risk inherent in the pensions business. It has noted that most of the OTC contracts available to manage these risks tend to be arranged with counterparties in the banking sector, which has been under stress recently. (i) Describe the main types of derivative instruments that can be used to hedge longevity risk. [5] (ii) Explain how counterparty risk originates in OTC contracts and how the insurance company can mitigate it. [4] (111) (a) Discuss the nature of the insurance company's LPI risk in a low inflation environment, commenting on potential ways of reducing it. (b ) Identify institutions that might be natural hedgers of inflation risk in the financial markets, commenting on how likely it is that they would want to use inflation derivatives