# Tag Info

5

Within the fixed income space, there's a lot of literature on PCA trading. The first 2-3 principal component factors (PCs) can typically explain 90-99% of the total variances in yield curve movement. It's also nice, because the first PC looks like a change in the overall level of the yield curve, the second PC looks like a slope change, while the third ...

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

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 ...

3

You're not the first to trip on this, and unfortunately the fact that the provided example is from a different era doesn't help. Quite simply, you're not writing rates correctly. The 5-years swap rate, 0.3523%, must be written in decimal form as 0.003523. The same goes for the deposit rates. As your code is now, you're writing that the 4-years rate is ...

3

fixedLegBPS is the basis-point sensitivity of the fixed leg, that is, how much its NPV changes when the fixed rate changes by one basis point: it's calculated as the NPV corresponding to a fixed rate of 1 bps. Since the NPV of the fixed leg is linearly proportional to the fixed rate, you can write the equation targetNPV : fixedRate = BPS : 1 basis point ...

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

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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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 ...

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

Why do you think this is not apropriate? Matlabs documentation for 1-D Data interpolation states that interpl1 using method spline is the right way to go: Spline interpolation using not-a-knot end conditions. The interpolated value at a query point is based on a cubic interpolation of the values at neighboring grid points in each respective dimension. ...

2

There is a market for inflation linked government bonds (some countries e.g. US,CA,UK,FR,Germany,...). There are various prices quoted. The price with inflation lift (the inflation that has accumulated since the inception of the bond) and the price without the lift reflecting future nominal interest and inflation. You can calculate the real yield to ...

2

If you want to discount the CF3 from 3 years in the future to today you should use (1 + 3yr spot rate)^3. There's no reason to use forward rates for that purpose. The forward rates should only be used for period-by-period discounting - for example, if you wanted to find the value after 3 years of a CF4 which occurs after 4 years, you would use (1+ 1yr ...

2

bootstrap fedfunds (ois ) swaps to get your discount curve (asuming your portfolio is usd, and is usd collateralised). strangely i dont see the data on the fed site. i see data on LCH's site: http://www.lchclearnet.com/asset-classes/otc-interest-rate-derivatives/volumes/settlement-prices-swapclear-global#usd to get libor projection curve, you need to ...

1

The 3M-6M basis swap rate should be ~ Forward$_3^6$ $$(1 + \delta Forward_0^3)(1+\delta Forward_3^6) = ( 1 + 2\delta Libor_0^6),$$ where $\delta$ is equal to 3 month. This gives you a way to calculate the rate.

1

It depends on the market you're interested in and what the curve is used for. To build the USD swap curve, for example, you've got a ton of information available from actively traded market instruments – fed funds futures (monthly), OIS (even finer details at the front end), Eurodollar futures (quarterly), basis swap, etc. All of these should be ...

1

Instead of the constant maturity series (which IMO would give only a few points), you could use the prices of ZCB to get the USD curve. They are available here http://www.wsj.com/mdc/public/page/2_3020-tstrips.html It might require some slight smoothing to get a clean curve. This is the best way I know to get a US Govt curve for free.

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Nowadays, government yield curves are customarily built with only coupon bonds. Zero coupon bonds (i.e., STRIPS in the US) are much less liquid compared with coupon Treasuries, and tend to trade very differently. If you plot a zero curve implied by coupon Treasuries vs yields of STRIPS, you'll notice that they can differ quite a bit in certain parts of the ...

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 $\textbf{T}$ ...

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

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 ...

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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.

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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 ...

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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.

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