# Tag Info

6

I like to present to you a slightly different approach: Historically, only one single yield curve was derived from different instruments, such as OIS, deposit rates, or swap rates. However, market practice nowadays is to derive multiple swap curves, optimally one for each rate tenor. This idea goes against the idea of one fully-consistent zero coupon curve, ...

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 ...

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 + ...

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

Standard 3m curve interpretation: H, M, U, Z = Mar, Jun, Sep, Dec IMM dates in the futures convention (see SRKX's answer), and 2Y would be just the calendar 2y point. Assuming that what you found was done in 11th July 2011: U1 21 Sep 11 - 21 Dec 11 (IMM = 3rd Wednesday to following IMM) Z1 21 Dec 11 - etc H2 21 Mar 12 M2 20 Jun 12 U2 19 Sep 12 Z2 ...

3

I think they are using the same convention as the future exchanges for delivery months. You can find a complete mapping on the wiki page. The letter corresponds to a month and the number corresponds to the last digit of the year. So for example to understand U1 you find U=>September and 1=>2011 (you have to "guess" the relevant decade, it's quite ...

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

To elaborate on Freddy's answer: These days you need to maintain a separate funding (usually OIS) curve to your Libor* type curves. Once you have this discounting curve, you can calculate from Libor instrument market data what the market estimations of that Libor are: 3m instruments like Interest Rate Futures, IRS with a 3m float leg, 3m FRAs can be used to ...

1

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 ...

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 ...

1

(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 ...

1

Not sure this includes all data but certainly interest rate swaps. I heard somewhere FED Saint Luis (or was it another office) actually offers an API into their public data center, but I cannot confirm that: http://research.stlouisfed.org/fred2/categories/32299

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