# 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 ...

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 23....

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

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

Given the Ho-Lee interest rate model of the form \begin{align*} dr_t = \theta_t dt + \sigma dW_t, \end{align*} the price at time $t>0$ of a zero-coupon bond, with maturity $T$ and unit face, has the form \begin{align*} B(t, T) &=E\Big(e^{-\int_t^T r_s ds} \mid r_t \Big)\\ &=e^{-(T-t)r_t - \int_t^T (T-u)\theta_u du + \frac{\sigma^2}{6}(T-t)^3}. \...

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

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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Per @dm63, these yield curves are basically smoothed curves that best fit the prices/yields of bonds traded in the secondary market. However, they reflect much more than market expectations. Refer to Deriving Interest Rates for details.

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Yes, yield curves are a pictorial representation of the current secondary market yields of government securities (gilts, in the UK). These market yields are determined largely by expectations about what the central bank will do to short term rates over time.

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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 ...

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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 (...

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This is all theoretical and real life will diverge from the theory The spot rates and forward rates are linked. Spot rate for the nth period should equal the product of all the forward rates up to that period. i.e Let Spot{n} = spot rate for nth period Let Forw{k,j} = forward rate to period j at period k Let X_m be the m'th period. Then (1+Spot{n})^n =...

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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 ...

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