Derivatives

You are the risk manager of a major UK bank which trades a wide range of fixed income products, including bonds, swaps and options. Define "market risk" and "credit risk". [2] Outline how you would measure market risk using: (a) a daily report of risk sensitivities against limits (b) a daily Value-at-Risk (9) a weekly stress test [7] (it) (a) Illustrate your answer to (ii) with reference specifically to a multi- currency portfolio of swaptions, i.c. options on LIBOR-based fixed- floating swaps. (b) Identify the source of credit risk in this portfolio. (4] [Total 13] Let f, g be two non-income producing securities which depend on a single source of uncertainty, with: df =ufdi + ofd= dg = ugdi +0.gd= Define 2, the market price of risk; as: where / is the risk-free rate, and let = / (a) Define a martingale. (b) Explain the concept of numeraire assets in the context of the securities p. f and g. [3] Using Ito's formula on In o, show that if 2. = o, , then o is a Martingale. [10] (iii) Suggest what might be meant by a security / being "forward risk neutral" with respect to a security g. (2]