# 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

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 ...

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

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 ...

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

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 ...

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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

Let $\delta$ be 3 month and consider points of interest $\{T_i\}_i$ evenly spaced with $T_{i+1} -T_i = 3 month$. The Forward Rate $F_m^n(t)$ from period m to n at time $t$ is defined by $$(1 + \delta (n-m) F_m^n(t)) = \frac{B(t,T_m)}{B(t,T_n)},$$ where $B(t,T_i)$ is the time $t$ value of a zero coupon bond that matures in $T_i$. A swap rate $S_m^n(t)$ a ...

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 ...

1

The short answer is - you need more data. If you want to build a full zero-rate swap curve, typically these curves go out to 30 years. In general, the front of the curve is made from LIBOR rates, which you have. Typically you don't see practitioners use anything past the 3M point but some will use up to the 6M point. For the 2nd part of the curve, from ...

1

Translate your forecast of yields into a forecast of bond prices: you believe long term bonds will fall in price rel. to short term bonds. So, what to do? Shorten the duration of your portfolio, i.e. sell long term bonds and/or buy short term bonds. Since you don't like long term bonds (and the fixed payments they make to you), you may also enter into ...

1

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

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 ...

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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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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 $\textbf{T}$ ...

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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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