2
$\begingroup$

I'm reading a book about interest rate modelling. It states the following formula

P(0,T) = exp(-sum of the forward rates)

But I thought it's the average of the forward rates?

enter image description here

$\endgroup$
  • $\begingroup$ Um, rotate picture first please? $\endgroup$ – BCLC Jul 25 '14 at 9:59
4
$\begingroup$

The price of the zero-coupon bond is the discount factor for this maturity. In the world of exponential compounding formulas are of the form $\exp(\sum \cdots)$. With a replication argument if we want to invest money for $n$ years what can we do. We invest for one year $r_0 = F(0,1)$ then after this year we invest for another year, the rate for this today is $F(1,2)$, after another year we invest again for one year, the rate for this today is $F(2,3)$. After all the discount factor is simply $$ \exp(\sum_{i=1}^n F(0,n-1,n)), $$ where the $0$ indicates that the forward rates are traded/observed at time $0$ and $n-1$,$n$ means that it is the forward rate for the respective year. So it is the sum, not the average.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.