Treasury Make Curve Bootstrapping
In the previous post discount canada goose online shop toronto for sale . we have introduced readers to basic principles of time value of money and presented Python implementation of the calculator. The time value of money is an essential principle applied in almost all areas of the financial mathematics. Today. we will discuss one of them - the basics of yield curve construction and bootstrapping canada goose online shop toronto for sale . Please note that full implementation of this example can be found here.
When calculating yield curves from market prices. the big question is which securities we should consider in the calculation. If we generalize the problem to a set of credit risk-free government securities. our choices will be as follows canada goose online shop toronto for sale cheap .
On-the-run securities are those which have been issued recently. thus the most liquid ones. Unfortunately canada goose online shop toronto for sale . there are often wide maturity gaps between them. Because of this. analysts often fill these gaps with additional off-the-run issues. For example. a 50-year bond issued 2 years ago effectively serves as a security filling the maturity gap of 48 years.
It is even possible to combine all on and off-the run securities in such a way they will expire on the same date. This will naturally lead to collisions in yields and maturities. which can be then aggregated and interpolated for even better results.
Another solution is to use treasury coupon strips. The coupon strip with a single payment is priced in a way which yields directly to the spot rate for given maturity. With this approach, canada goose stockists montreal online store . the bootstrapping process discussed later will not be necessary. However inexpensive canada goose online shop toronto for sale , canada goose retailers in quebec sales . the drawback using coupon strips is different tax treatment skewing the whole calculation.
With respect to the facts above and for the purpose of this simple example. we will be using on-the-run market prices of UK Gilts. as of 19th of September 2012. The quoted gilts span maturities from 6 months to 48 years. sufficient enough for the sake of this analysis, canada goose chilliwack parka womens online store . The relevant prices were obtained from www. bondscape. net and look as follows.
Calculated yields to maturity don't necessarily correspond to those quoted in data file due to accrued interest and a fact that coupon payments are bound to specific calendar date. which is not necessarily one semi-annual period from now.
The code performing the calculation in Python would look as follows. The input is a set of bonds canada goose online shop toronto for sale . each with given maturity canada goose online shop toronto for sale buy . price and coupon rate. These values are passed into the TVM calculator introduced in one of the previous articles to calculate the bond's yield to maturity.
These yields. together with maturities are then aggregated in lists tr (time to maturity) and yr (yield to maturity)
As the time passes. the maturities of all issues are shortened by one day each day. However. if we want to compare the same yield curve across different dates. the maturities must match. Hence. we need to interpolate and normalize all yield curves into a common set of maturities. e. g. 1m. 3m. 6m. 1y. 2y. 5y and etc.
On the other hand. for the purpose of bootstrapping real canada goose hologram sticker . it would be convenient to interpolate all maturities into a scale with annual intervals. such as from 1 year to 40 years canada goose parka eu online store . Therefore. we will go this way.
The interpolation is performed in Python automatically using SciPy's interp1d command. Apart of the linear interpolation. it provides few others. such as nearest canada goose snow mantra sverige . cubic or quadratic canada goose borden bomber jacket sales . Unfortunately this algorithm is not able to interpolate outside the initial range - this could be problematic especially for short-term maturities. such as 1 month canada goose online shop toronto for sale .
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