14A [ 4 + 2 + 2 + 4 + 4 ] The CCIL fitted the zero coupon yield curve on 26 Sep 2018 to a Nelson-Siegel style model, and finds the following parameters: Date Bo Bi B2 26-Nov-2018 7.7474 -1.1283 1.7837 4.4442 T f(m) = Bo + Bi exp(-m/T) + **B2 *exp(-m/T) T m T m f(u) = 7.7474 - 1.1283 exp(-m/4.4442) + 1.7837 exp(-m/4.4442) 4.4442 a) Why do we prefer the Nelson-Siegel approach to polynomial regressions of the form f(m) = a +bm+c. m+ dem? b) What is the 100 year rate (long run rate )? c) What is the overnight rate ? d) Derive analytically that the location of the unique interior extremum is B2-Bi B2 e) Sketch the zero coupon yield curve (please be neat ). m -T or 14B 4 + 2 + 2 + 4 + 4 a) Suppose we have a single source of risk in an economy. The asset returns of 2 assets follow processes driven by this common source of risk dW dr = 0.08.dt -0.2. W dra = 0.12.dt-0.4.dW 1) Construct a portfolio of these 2 assets that is riskless ii) What is the risk-free rate of return? iii) What is the market price of risk" in equilibrium? b) Suppose we have a model of the short rate where dr, -0.25% dt+1%.(/6%)-dW,, where dW, ~ N(o, vdt) 0.25% and 1% are the annualized drift and standard deviation . Suppose the initial short rate is 6%, and we try to model this short rate with steps of one month i) Sketch a 2-month tree of short rates, ii) List any two distributional properties of the short rate implied by such a model, stating whether this property is desirable or undesirable. 14A [ 4 + 2 + 2 + 4 + 4 ] The CCIL fitted the zero coupon yield curve on 26 Sep 2018 to a Nelson-Siegel style model, and finds the following parameters: Date Bo Bi B2 26-Nov-2018 7.7474 -1.1283 1.7837 4.4442 T f(m) = Bo + Bi exp(-m/T) + **B2 *exp(-m/T) T m T m f(u) = 7.7474 - 1.1283 exp(-m/4.4442) + 1.7837 exp(-m/4.4442) 4.4442 a) Why do we prefer the Nelson-Siegel approach to polynomial regressions of the form f(m) = a +bm+c. m+ dem? b) What is the 100 year rate (long run rate )? c) What is the overnight rate ? d) Derive analytically that the location of the unique interior extremum is B2-Bi B2 e) Sketch the zero coupon yield curve (please be neat ). m -T or 14B 4 + 2 + 2 + 4 + 4 a) Suppose we have a single source of risk in an economy. The asset returns of 2 assets follow processes driven by this common source of risk dW dr = 0.08.dt -0.2. W dra = 0.12.dt-0.4.dW 1) Construct a portfolio of these 2 assets that is riskless ii) What is the risk-free rate of return? iii) What is the market price of risk" in equilibrium? b) Suppose we have a model of the short rate where dr, -0.25% dt+1%.(/6%)-dW,, where dW, ~ N(o, vdt) 0.25% and 1% are the annualized drift and standard deviation . Suppose the initial short rate is 6%, and we try to model this short rate with steps of one month i) Sketch a 2-month tree of short rates, ii) List any two distributional properties of the short rate implied by such a model, stating whether this property is desirable or undesirable