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1

Back when I had lots of free time, I used to publish a series of constant maturity par bond total return indices (http://hungrydummy.com/datacenter/). Because these are "par" bonds, they are immune to coupon effects. I briefly described the computational methodology on that page, which is copied below. The same methodology can be used to create constant ...

1

A simple example might help. You need to transform your coupon bonds in equivalent zeros. Imagine that you have 5 coupon bonds and you are at the end of 2011: Coupon, Maturity, Price = 5.25% 2012 101.69 Coupon, Maturity, Price = 4.5% 2013 101.52 Coupon, Maturity, Price = 5.5% 2014 104.49 Coupon, Maturity, Price = 5% 2015 103.35 From the first one you can ...

2

Zero coupon rates are outputs, not inputs. As mentioned in the other post, given the parameters (say the initial guesses), you can easily compute the theoretical prices of each bond, which can then be converted into their theoretical yields (standard price to yield conversion). You should minimize the residuals between these theoretical yields and the market ...

1

You really don't even need to put them into matrices, which I feel is confusing you more than helping... For each bond, you have a list of cash flows ($c_i$'s). For each cash flow, you can compute the corresponding discount factor ($d(t_i)$'s). Sum up the discounted cash flows gets you the theoretical price: $P = \sum_i c_i d(t_i)$. Repeat this for every ...

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It is simply the difference between "today" and the cash flow date in years. A 30-years bond paying semi-annual coupons has 60 cash flows, and each cash flow has its own "TTM".

3

Jojo, once again the paper is about Nelson-Siegel and not Nelson-Siegel svensson (the former allows for one hump whereas the latter for two humps). Jojo, in practice people often start by fixing $\lambda$ then estimate the model by OLS and check the squared errors of the model. Then change $\lambda$ and repeat the procedure. This is highly efficient, and ...

1

Say at time $t$ , the cash flows of some bond $b$ can be described by the two vectors $\textbf{c}$ and $\textbf{t}$, containing information about the value of the nominal cash flows and cash flow times in years, respectively. Similarly, if we have a range of bonds $B = \{ b_1, ..., b_n\}$ that trade on a market, the matrices $\textbf{C}$ and $\textbf{T}$ ...

0

if I read it correctly the paper you mention is about Nelson-Siegel and not Nelson-Siegel Svensson. The easier way to cross check it is to simply start by fixing theta and estimate the remaining parameters by OLS. If that works, then the optimization algorithm should work similarly. Below I attach a simple matlab code that does it and that you can adapt for ...

2

EONIA swaps stopped trading some time in 2014. Since it stopped trading, it does not make sense to remember when it stopped trading :).

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There are many ways to bootstrap the Treasury curve. I'll start by talking about my personal preference. The key step is to select appropriate securities to be included in the procedure. My preference is to use 60 Treasuries that are spaced out evenly (i.e., maturing 6 months after each other). Specifically for US Treasuries, it is convenient to select ...

1

By multiplying the transpose of $A$ to both sides, you can make it to be a square matrix. That is $$A^T A P = A^T F.$$ Moreover, if $A^T A$ is invertible, you can have that $$P = \big(A^T A\big)^{-1}A^T F.$$ In general, for a non-square matrix, or a square matrix, $A$, but not invertible, the singular value decomposition approach can be employed. See the ...

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