What's new

# derivative coupon bond

#### haroun

##### New Member
Hey @David Harper CFA FRM I have problem with derivative (coupon BOND) I tried to make the first derivative the second derivative but I could not get to the same results.

we have a coupon bond that matures in T periods with as the face value, c is the coupon rate and rentabilite the profitability at maturity. r=yield

The price of this obligation is : P= cF/r * (1-(1+r)^ -t)+F/(1+r)^T

Check (by rigorously justifying your calculation steps) that the dollar duration is given by

DD= cF/r^2 *( 1- 1+rT+(1+r)^ -1/(1+r)^T ) + TF/(1+r)^T+1 (dollar duration )

and dollar convexity

DC= cF/r^3 *(2- 2*(1+rT(1+r)^ -1)+T(T+1)r^2*(1+r)^ -2 / (1+r)^T ) +T(T+1)F/(1+r)^T+2 thank you .

#### Nicole Seaman

Staff member
Subscriber
Hey @David Harper CFA FRM I have problem with derivative (coupon BOND) I tried to make the first derivative the second derivative but I could not get to the same results.

we have a coupon bond that matures in T periods with as the face value, c is the coupon rate and rentabilite the profitability at maturity. r=yield

The price of this obligation is : P= cF/r * (1-(1+r)^ -t)+F/(1+r)^T

Check (by rigorously justifying your calculation steps) that the dollar duration is given by

DD= cF/r^2 *( 1- 1+rT+(1+r)^ -1/(1+r)^T ) + TF/(1+r)^T+1 (dollar duration )

and dollar convexity

DC= cF/r^3 *(2- 2*(1+rT(1+r)^ -1)+T(T+1)r^2*(1+r)^ -2 / (1+r)^T ) +T(T+1)F/(1+r)^T+2 thank you .
Hello @haroun