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## #1 2006-03-15 02:19:13

naks
Member
Registered: 2006-03-15
Posts: 2

### Differentiation question

If the price of a bond can be written as the present value of its coupons and principal where:

P= C * [ [ (1 -  1 / (1 + y)^n ] / y] + [ A / (1+y)^n ]

where C is the semi-annual coupon, A the principal and y is the required yield.

(a) what is the the derivative of this expression with respect to its required yield.
(b) Derive an expression for modified duration.
(c) Hence derive an expression for the convexity measure.

Last two parts are a mathematical-finance based questions. 1st part is standard differentiation.

Can any one help me with any any part of this question??

Thanks!!

Last edited by naks (2006-03-15 02:52:36)

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## #2 2006-03-15 06:21:38

ryos
Member
Registered: 2005-08-04
Posts: 394

### Re: Differentiation question

The derivative I can do, but nothing else.

That is, assuming A and C are constants. If they aren't, the implicit differentiation is a bit more complicated, but manageable.

El que pega primero pega dos veces.

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## #3 2006-03-22 02:41:58

naks
Member
Registered: 2006-03-15
Posts: 2

### Re: Differentiation question

sorry for the late post - but thankyou so much for your help!!

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