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8

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 ...


6

There are many reasons why a yield curve can be inverted. A default-free yield curve reflects a combination of - market expectation of future short-term interest rates; bond risk premium: usually positive, longer duration bonds are more volatile and riskier, so investors demand a compensation in the form of higher yields; convexity. Let's consider a case ...


4

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 ...


4

US Treasuries start trading BEFORE they're actually issued, in the so-called "When-Issued" market. This market allows investors to purchase the new issues for "forward settlement." Because these bonds haven't been issued, they have no coupon rates and are traded on a yield basis. On a daily basis, market forces drive the yields, until the auction date. On ...


4

Libor includes risk. It is riskier to make a 6m loan than two 3m loan. So the 6m Libor curve is not the same as the 3m one. Ther difference is the basis spread. When using a short rate model, you are modelling one curve. As a first approximation, you can deduce the other curves by adding a deterministic basis spread.


4

This is what banks have been doing for hundreds of years. They borrow short term (mainly through deposits and interbank lending) and lend long term (e.g. mortgages). I would not call it arbitrage, as it is not riskless profit. Apart from credit risk and interest rate risk, there is also liquidity risk. In these type of strategies, the investor has to ...


3

This is actually only true when the yield curve is upward sloping. Intuitively, zero rates are average forward rates; e.g., the 10-year zero coupon yield is the geometric average of the 0y forward 1y rate, 1y forward 1y rate, 2y forward 1 year rate, ..., and 9y forward 1y rate: $$ (1 + y_{10})^{10} = (1 + f_{0,1})(1 + f_{1,2})\ldots(1 + f_{9,10}). $$ So ...


3

Inverted curves (typically) appear when the economy is overheating. There is full employment but investment demand is still there and it is creating inflationary pressures. The central bank increases the short rate (which is their classical policy instrument) to take money off the table and cool down investment demand. However, the market knows that this is ...


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

@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 ...


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 ...


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 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

I'll assume the rest of the world doesn't have access to a similar oracle. Indeed if it did future returns would converge to the risk free rate instantly. In this case, I would prefer holding the AAA bond instead of the stock because the rest of the world would consider it to be much less risky. As a financial institution, reducing the risk of your ...


2

Libor is indeed usually fixed in advance (and paid in arrears). Thus, in your example the first fixing date will be 2 business days before March 5th, and the second fixing date will be 2 business days before June 5th. Usually, therefore, the first fixing is already known when the swap is traded. You say that the Libor leg is paid semi-annually - that's not ...


2

while it is true that $$\lim_{T\to\infty} Z(t, T) = \lim_{T\to\infty} e^{-r(T-t)} = 0$$ this is when $r$ is independent of time to maturity, a flat and constant yield curve. In practice, we use yield curves which vary depending on what day they are estimated and what maturity the ZCB is. If in fact $r(t, T)$ depends on today and the maturity then the ...


2

This is something that banks don't do very well (in my opinion), but we can look to the insurance industry for help. Insurance liabilities often span decades, and the regulation has come up with something called the Ultimate Forward Rate (or UFR). It's currently a hotly debated topic with the advent of Solvency II (insurance regulation) coming into effect ...


2

While @Baruch Youssin answers correctly in the general sense, the first part of his answer isn't what happened in the example code. While QLNet is a port of QuantLib, it's not a direct port. Your quoted example doesn't show up in QLNet. The example in QuantLib was written in a very complicated way, in fact it's a simple example. discountingTermStructure is ...


2

I do not yet know QuantLib but one question is general and easy to answer: My first question is why do they use different yield curve? These two curves differ by risk levels inherent in them - the credit spreads over the risk-free yield curve (e.g., the OIS curve). The discounting curve, discountingTermStructure, embeds the risk that this particular ...


2

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


2

You wrote Given this, what does the value of 1M LIBOR curve at 1Y point represent? It is a real number X such that: The following deal can be agreed today in the swap market: You will pay me the amount X (fixed in advance) one year from now, and in return I agree to pay you one year from now the amount Y equal to the 1 Month Libor Rate published at that ...


1

Your question is really about how to map between term-to-maturity and calendar dates, which can be a tricky problem since the number of days in a month varies by month. In short, you should increment using months if your incremental term is in months, and increment using years if your incremental term is in years. In your examples, three months (or 0.25 ...


1

Here you can find what you need for. It explains how to build & price a basis swap curve in a step-by-step procedure. The link leads on the 2nd page to the guide (relative to the question), but, I suggest you to start from the 1st post.


1

Usually yield/time is the standard context for definition of a yield curve, with yields being derived from prices (of interest rate instruments) for certain maturities (times). The investopedia article you are referencing is all about the yield/price connection (since duration and convexity represent first and second order "price" sensitivity measures to ...


1

First, it's not true that a market sector is cheap whenever the forward curve lies above the par curve. In fact, whenever the yield curve is upward sloping, the forward curve will always lie above the par curve. Conversely, when the yield curve is downward sloping, forwards will always lie beneath the par curve. In the example you quoted, Ilmanen chose a day ...


1

Obviously a perfect forecast for interest rates is a bit hard to come by, such a thing would make the inventor quite a tidy sum. Broadly, the task you're seeking to accomplish falls under the banner of yield curve modeling, and there is a very substantial body of research in this area, including several good books. There are some canonical examples of ...


1

Generally it is best to use the rates that best capture how the collateral of the instruments are priced. If the overnight collateral on the instruments is managed using offshore JPY depo, then this would be a good choice.


1

Your second version is correct. The market determines the price of these bonds, from which the curve is derived. Your first version has a tiny speck of truth, in the sense that the central bank (e.g. the Fed), which is a 'government organisation' has been recently interfering with the bond market in order to affect the yield curve (so called 'operation ...


1

The yield curve gives you the tools to calculate everyhing that is derived from it. Derivatives from the yield curve only are e.g. - Fixed rate bonds - Forward Rate agreements - Floaters - Swaps. All these are discounted cashflows or portfolios based on discounted cashflows and forward rates (which you can calculated from the yield curve). If you ...



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