Estimating Yield Curve
Overview
It is well known that the rate of interest one can obtain when borrowing or lending will in general
be dependent on the period over which the money is lent. If one plots rate versus period, one obtains
a curve.
Of course, there are complexities to building a curve from market data.
- On any given day you may multiple instruments with cash flows or maturing on that day, however, they may have differenct
credit risk
or tax treatment which affect the price. Any process that builds a curve from these must deal with these affects.
- A price for every day along the curve may not be available. That means some degree of interpolation must be utilized to fill in the missing dates.
Bootstrap
Bootstrap :
The bootstrap is a method to determine a set of discount factors to
apply at a given set of dates, when prices are available for instruments
with cash flows (coupons and principal, for example) on those dates.
Function Approximation
The bootstrap method is a simple method to get a discount rate at a
specified number of dates. However, when evaluating fixed income instruments,
it is often necessary to be able to get a rate for a date that exists
between two dates in list. The way this is done is to fit a curve between
the points that are estimated using the bootstrap procedure. This can
be accomplished in any number of ways using
approximation.
The most prominent method is the use of splines to fit a smooth curve to the
bootstrap points.
