Instruction: You have been retained by the treasury department of SHB-Brooklyn corporation to price derivative securities. The CEO and CFO of the company plan to issue 5 year and 15 year corporate bonds to raise capital and ask you to suggest fair values of the newly issued bonds as of 04/09/2019. Thus, you now plan to implement five term structure models ( Cubic-Spline, Nelson-Siegel (NS) yield curve model, NelsonSiegel-Svensson (NSS) yield curve model, Vasicek Model, and CIR Model) and price bond instruments using these models. Problem 1. Go and visit U.S department of treasury website 1 and obtain the yield rate on 04/09/2019 from U.S. department of treasury.

1https : //www.treasury.gov/resourcecenter/datachartcenter/interestrates/P ages/T extV iew.aspx?data = yield 1

1) Plot the yield rates over time to maturity and explain the shape of the curve.

2) Using the cubic spline model, which is given by y(t) = 0 + at + bt2 + ct3

estimate 0.5 year, 1 year, 1.5 year, 2 year, . . ., 10 year yield rates.

3) Plot a combo chart to show how well the estimated yields from the cubic spline model fit the original yields.

4) Compute two semi annual coupon bonds, 5 year semi-annual coupon bond with a coupon rate of 3.7% and 10 year semi-annual coupon bond with a coupon rate of 4.8% assuming a face value of $ 1,000 and continuously compounding rates. P = X T t=0.5 CF(t) e y(t)t

Where: P represents the price of a bond. CF(t) represents a bond's cash flow at time t.

5) Compute each duration and convexity for the 5 year and 10 year bonds. D = X T t=0.5 t CF(t) e y(t)t P (3) C = X T t=0.5 t 2 CF(t) e y(t)t P

Where: D represents the duration of a bond. C represents the convexity of a bond.

I did the first first one.