What is the difference between real income and nominal income.
A central counterparty (CCP) is setting the initial margin requirements for interest rate derivatives by modelling the behaviour of interest rates in the future. It wishes to carry out scenario analysis. The CCP proposes to use the Vasicek model for interest rates. (1) Describe why the CCP should carry out both real-world and risk-neutral projections of interest rates. [2] (ii) Write down the stochastic differential equation (SDE) of the Vasicek model in the real world, defining all terms used. [2] (iii) Describe how the CCP could calibrate the parameters of the real world SDE in part (ii). [2] (iv) Define the market price of risk for an interest rate derivative , including equations and defining all terms where appropriate. [2] (v) Show how the risk-neutral SDE for the Vasicek model can be derived from the real-world SDE for the Vasicek model and the market price of risk. [2] (vi) Explain why the Hull-White two-factor model may be more appropriate than the Vasicek model for the CCP's purpose. [4] The CCP has derived the following levels of initial margin for both payer and receiver swaps for all counterparties. All initial margin will be cash only. Term outstanding on Level of initial margin required for swap payer and receiver swaps Less than 5 years 1% of notional More than 5 years 2% of notional (vii) Assess how effective these initial margin requirements will be for mitigating counterparty risk to the CCP from a counterparty with a range of payer and receiver swaps. [5]An investor holds 100 shares in a company. The current share price is 46.25 per share. There are two traded option series which expire in nine months. The deltas and gammas of the option series are given below: Strike = 40 Strike = 50 Call Put Call Put Delta 0.8018 0.1982 0.4276 0.5724 Gamma 0.0278 0.0278 0.0392 0.0392 Each option is written on the same share as the investor holds. Throughout this question you can assume that any expenses and transaction costs can be ignored. (1) Determine how the investor can make the portfolio delta and gamma neutral by calculating the number of call options to hold, to the nearest integers. [3] (ii) Determine how the investor can make the portfolio delta and gamma neutral by calculating the number of put options to hold, to the nearest integers. [3] (iii) Contrast the effectiveness of the delta and gamma neutral hedges in parts (i) and (ii) when there is a large fall in the share price. [2] (iv) Show that the put portfolio is less effective than the call portfolio when the share price is less than 15.6 (rounded to one decimal place), assuming no rebalancing to the portfolios. [2]
