Question

It is a product that pays $100 face value, three years maturity, 12% annual bond yield (based on continuous compounding), and pays $5 every three months. At this time, when the bond yield increases by 0.1%, calculate the bond price using the duration. Also, compare it with the price of the bond obtained by the general method of evaluating the bond by discounting it at the rate of return

Answer 1

Ans:price of bond = $5/1.1.2 + $ 5/ (1.12)(1.12) + $5+$100/ (1.12)(1.12)(1.12)

= $83.18

Volatility= Duration/ 1+ yield of bond

= 3/ 1.12

= 2.678%

when increase in 1% , price of bond decrease by 2.678%

when increase in 0.1%price of bond decrease by 0.1*2.678%

Therefore value of bond decrease by .2678%

price of bond = 83.18 - .2678% *83.18

= $82.95

As per general method of evaluating by dicounting with rate of return:

price of bond = $5/1.1.201 + $ 5/ (1.1201)(1.1201) + $5+$100/ (1.1201)(1.1201)(1.1201)

= $ 82.95