Enterprise Risk Management Formula Book
7. Interest rates and bond pricing
[this page | pdf | back links]
7.1 Spot and forward rates
Suppose is the price at
time 0 of a zero-coupon bond that pays 1 at time ,
is the spot rate
for the period , i.e. 0 to ,
and is the
instantaneous forward rate at time 0 for time (where
and are both
continuously compounded) Then:
7.2 Duration,
modified duration, (gross) redemption yield (yield to maturity), credit spread,
option-adjusted spread, annualisation conventions
If a bond gives the holder entitlements to cash flows at time (and
is assumed not to be subject to default risk) and has a ‘dirty price’, ,
then its (gross) redemption yield (yield to maturity) is the (sensible) rate of
interest that equates with its present
value, i.e.:
Its duration is then and its modified
duration is . is almost exactly
the same as its PV01, also called DV01.
Its credit spread is the difference between its (gross)
redemption yield and the corresponding yield on a reference security, often a
corresponding government security providing the same cash flows in the event of
non-default. The option-adjusted spread is the corresponding spread taking into
account optionality in the bond in question and/or in the reference bond.
Interest rates may be expressed as
annual rates, , semi-annual
rates, , quarterly rates, , monthly rates, or even
continuously compounded rates, , where:
The quotation convention of a bond (e.g. ACT/ACT) defines
the amount of accrued interest payable when a bond is bought or sold in between
coupon dates.
NAVIGATION LINKS
Contents | Prev | Next