Question

Consider a 2-year coupon bond that pays coupon annually with a coupon rate of 3%, face value $1000, a yield to maturity of 4%.

(a) What is the approximated bond price estimated by duration if the yield is increased by 0.5%?

(b) What is the convexity of this coupon bond?

Answer 1

1.
Price now=1000*3%/1.04+(1000*3%+1000)/1.04^2=981.1390533

Duration=(1*1000*3%/1.04+2*(1000*3%+1000)/1.04^2)/981.1390533=1.970599321

New Price=981.1390533*(1-1.970599321/1.04*0.5%)=971.8437074

2.
Convexity=((1^2+1)*1000*3%/1.04+(2^2+2)*(1000*3%+1000)/1.04^2)/981.1390533*1/1.04^2=5.438606958