# Tag Info

7

Garabedian, Typically, the "swap curve" refers to an x-y chart of par swap rates plotted against their time to maturity. This is typically called the "par swap curve." Your second question, "how it relates to the zero curve," is very complex in the post-crisis world. I think it's helpful to start the discussion with a government bond yield curve to ...

7

There are two parts to your question and I'd like to answer them separately. Curve Construction On a daily basis, you can observe prices on a large variety of instruments, whose prices are driven by news and trading flows. Based on market prices of these instruments, there are a number of ways to create discount curves/forward curves. At a very high level ...

5

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

I think what you wrote is correct. I'll rephrase everything according to my way to give you another point of view. The price of a coupon bond at time $t = 0$ is the sum of the discounted cashflows given by the coupons and the face value: $$P_0 = F \cdot D(0, T_n) + \sum_{i=1}^{n} 11.04\% \cdot 0.5 \cdot F \cdot D(0, T_i)$$ where $F$ is the face value, ...

3

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 ...

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 ...

2

@Arrigo's answers are quite good; I'll try to beef up his points a bit more. Yield curves should be constructed using instruments of similar credit risks. If you're building a US Treasury yield curve, then you should use Treasury bills, notes, and bonds (although lots of people actually exclude Treasury bills because of market segmentation concerns). On ...

2

In this context, I believe carry refers to the sum of "pure" carry + roll down. Carry, in the most general sense, is the return of a position in a static world; i.e., assuming time is the only variable that is changing, what's your holding period return on a trade? When you buy a bond, the "total carry" is the sum of 1) "Pure" carry – you get interest ...

2

Predictability - we all know what a bootstrapped curve will do when we shift a value. A minimisation, however, could jump to a new minimum at any moment. They also have unpredictable performance; sometimes a minimisation is fast, sometimes slow. Robustness - these codes have been around forever, and they work. New codes, not so much. Defendability - why is ...

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

I don't think they are implying that future interest rates are predictable. They may be speaking of implied forward rates as predictors of future rates or, generally, of the yield curve as an expectation of the future path of short-term interest rates. If $P(0,T_1)=1/(1+r_1)$ and $P(0,T_2)=1/(1+r_2)$ are the prices today of two "risk-free" zero coupon bonds ...

2

The important thing to know is that the par curve, the zero curve, the forward curve, and the discount curve are just transformations of each other; they contain exactly the same information (see What is the Swap Curve?). I think the confusion arises because many books tell you to connect the yields to maturity of benchmark bonds and call it the par yield ...

2

The NS model should be fit directly to bond prices. If you have the prices of all the Treasuries, you should use those directly. See this paper for how the Fed does it http://www.federalreserve.gov/pubs/feds/2006/200628/200628pap.pdf The "Daily Treasury Yield Curve Rates" are already fitted par yields (they're fitted using a cubic spline model to on-the-run ...

1

I would put it a bit differently. You can do 2 things: Either you apply an optimization/fitting procedure that has all the bond prices as inputs and zero rates for the chosen maturities as outputs. The objective function is the deviation between the discounted (by the to-be-found zero-rates) cashflows of each bond and the traded bond prices. To find a ...

1

How are the future interest rates determined? Two ways. 1) They are observed in the market, i.e. they are the best estimate of the market participants. One way is to use Bloomberg. 2) You can create your own discount curve and from that calculate the forward rates. Discount and forward curves for non-collateralized swaps must be consistent, otherwise ...

1

For the US Treasury market, zero coupon bonds are traded and they are called STRIPS. You can access them through "S GOVT" (coupon Strips) or "SP GOVT" (principal strips) on BBG. With regard to relative value trading, it's actually pretty rare that we fit models to zeros, because a lot of them are not liquid and trade differently from their coupon ...

1

For RV purposes, I have actually continued to use libor discounting for simplicity; otherwise, you'd have to model multiple curves, which become very difficult to work with... That being said, the curve has been trading very differently after the crises. For example, 5y typically didn't deviate that much from 2y and 10y on relative value basis historically, ...

1

I'll try to give you an answer. I think the term structure is built from those financial products because they are the most liquid for those maturities: theoretically, a liquid instrument has a price coming from a large consensus which you can think of the market. This is an "academical" reason, probably there are other reasons also (I'm still learning). ...

1

There is a new book about this new topic: http://www.amazon.com/Interest-Rate-Modelling-Multi-Curve-Framework/dp/1137374659 The author is a leading developer in Opengamma. Opengamma does have support for multi-curve building.

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 ...

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