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6

Your observations are pretty much correct. The groupings are because of the fine print "Note how I have expanded the drift and volatility terms at $t = T$; in the above these are evaluated at $r$ and $T$." on the same page (p.528). Basically, $w$ is a function of both $r$ and $t$. Since we want to use $w(r,T)$ instead of $w(r,t)$, we taylor expand ...


5

Ok, I've done some digging in the code. It's an issue with the LogLinear interpolation; while trying to find the correct rate for the 1-week node, the bootstrapper wanders unchecked into a region of negative rates and the logarithms blow up. At this time, I'm afraid the workaround is just to use some other interpolation. Or recompile the library and the ...


5

There's no class at this time to add two curves as you want, but it won't be much difficult to write it. The closest you'll get in the library is the ZeroSpreadedTermStructure class, that shows the general idea: it inherits from YieldTermStructure (by way of ZeroYieldStructure) takes a YieldTermStructure and a spread (constant, in this case) and override ...


4

Quantlib supports multi-curve framework (to the best of my knowledge). By the way, there's a "newer" version of that paper (authored by Pallavicini & Brigo). http://arxiv.org/abs/1304.1397 This paper might also be useful for you, very practical and basically answers any question you could have. Also see this discussion about multi-curve discounting ...


3

It's hard to be sure without seeing the inputs, but I'm guessing that the implied curve changes shape because the original curve does (which you can see from your output: except for the 1-year and 5-years points, the actual discounts are different). The reason the original curve changes is probably the different position of weekends or holidays (so that, ...


3

(In addition to the answers of Freddy and Phil H): With "modern" multi-curve setups: You have to distinguish between discount curves (which describe todays value of the a future fixed payoff (e.g. a zero coupon bond)) and forward curve, which describe the expectation (in a specific sense) of future interest rate fixings. Swaps pay LIBOR rates and are ...


3

As @michipilli said, if $Z = 1+ as + bs^2 + cs^3$ (where I have substituted $T-t$ by $s$ for ease of notation and also suppressed the dependencies of $a$, $b$ and $c$) and $\log (1+\zeta) = \zeta - \frac{1}{2}\zeta^2 + \frac{1}{3}\zeta^3 + ...$ then, \begin{align*} \log Z &= (as + bs^2 + cs^3) - \frac{1}{2}(as + bs^2 + cs^3)^2 + \frac{1}{3}(as + ...


2

I think the following two questions and related answers should help in answering the question: Why use swap-rates in a yield curve? and Is there an Australian Interbank Rate? Essentially to derive funding curves you gotta use what is left with the constraint that the source instrument has to be liquid enough and closely enough reflect true market ...


2

The book by Francis Diebold & Glenn Rudebusch "Yield Curve Modeling and Forecasting" addresses both a dynamic extension of Nelson-Siegel and an arbitrage-free version - may be helpful for what you are looking for. Link below: ...


2

If you look at wikipedia then you find the definition that a par-yield is the coupon rate, such that bond prices are $100$. This is the definition. Consider $N$ bond with a given coupon rates $c_i$, times to maturity $T_i$ prices $P_i$,for $i=1,\ldots,N$. Then you can calculated the yield-to-maturity for each bond $y_i$. Some mathematics reveal that a bond ...


2

Your steps 1. to 3. sound reasonable. I am not sure about industry practice (what industry?) I always do step 1. using PCA on historical correlations. If you plan to do a regulatory exercise better check with your regulator what he prefers. Most interesting to me is step 4. which - I think - is in general impossible to do. This can be achieved only in very ...


1

Your overall approach is correct. However to my knowledge it is formally more appealing to work with a parameterized and smoothed yield curve. Basically one assumes that the yield curve can be described by a smooth function $r(t,\alpha, \beta,\gamma)$ (mostly of three parameters) Given a set of market data $Y(t,T_1)\dots Y(t, T_n)$ one looks for ...


1

Assume we have $r(t)$ continuously compounded spot rate for maturity $t$. The price of the 2-year bond with semi-annual coupon $C$ is known to be $P$. We already have $r(0.5)$ and $r(1)$. We need $r(2)$ and $r(1.5) = f(r(1), r(2))$. Then $$ P = C [e^{-0.5 \times r(0.5)} + e^{-r(1)}+e^{-1.5 \times r(1.5)}] + (1+C)e^{-2 \times r(2)} $$ Using linear ...


1

In the United States, the Federal Reserve is always late to adjust to rising inflation with an extreme outlier in the mid-1990s. Inflation always leads the flattening of the yield curve since the Fed raising interest rates which flattens the yield curve is usually in response to rising inflation. Poorly managed currencies or even the US in the 1970s will ...


1

Is the author taking logs (and dividing by (T-t) etc) of our previous Z expansion from the previous page? He does, as you will see if you try to do the computation. What did you prevent to find this out by yourself? (I am trying to be constructive.) Mathematically, it doesn't add up to what the author provides as the answer. What am I missing here? ...


1

It really depends on how/where do you plan to use final values. I would not use extrapolation since it will ignore market realities. Forward rates across long end tend to be increasing while dumb extrapolation might give you the opposite result. In case of treasuries one can use treasury and swap spread and while you do not have 50 Y treasuyy one can find ...



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