0
$\begingroup$

In Hull's book (9th edition), on page 83, there is a simple example of par yield: par yield example

I am a bit confused when it says "this has semiannual compounding because payments are assumed to be made every 6 months. With continuous compounding, the rate is 6.75% per annum." Isn't the rate of 6.87% already assuming continuous compounding and is obtained by solving the equation here? What does it mean with continuous compounding, the rate is 6.75% per annum? Where is this coming from? And when it says "this has semiannual compounding", what is it referring to?

$\endgroup$
2
$\begingroup$

The way I like to explain this is with a notion of quoting. It's a convention to quote the coupons annualized by multiplying them by frequency. Suppose, the coupon is semiannual and equal to 3.375% of the outstanding. This is how much interest is accrued during 6 months. However, it is the convention to quote it on annualized basis, i.e. multiplied by 2 since it's semiannual. So, the coupon is quoted as c=6.75%.

Compounded, this coupon will yield the following in one year: $$(1+c/2)^2=1+y$$ $$y=(1+c/2)^2-1\approx 6.86\%$$

Alternatively you can quote the same yield on continuous compounding base: $$(1+c/2)^2=e^y$$ $$y=2\ln (1+c/2)\approx 6.64\%$$

$\endgroup$
5
$\begingroup$

c is the coupon of the bond, so it is paid semiannually. You can see this from the LHS of the first equation, which is the sum of present values of the coupons and principal. The 6.87 and the 6.75 are related by

$$ (1+6.87/200)^2 = e^{0.0675} $$

$\endgroup$

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