# Tag Info

## Hot answers tagged fixed-income

7

It is helpful to think of the yield $r_b$ of a risky bond (say a corporate) in your country as the yield of the risk-free government bond $r_f$ plus a "spread" $r_s$ ($r_b = r_f + r_s$). This extra spread is the extra yield that the market needs to be paid to purchase the corporate bond instead of buying an equivalent amount of risk-less bonds. In other ...

7

Treasury futures are actually really complicated... There are complete books dedicated to this topic (e.g., The Treasury Bond Basis) and really good sell-side research papers ("Understanding Treasury Bond Futures" by Salomon Brothers) that I highly recommend. You're actually very much on the right track, but I'll try to paint a somewhat complete picture. ...

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

you can view a bond as a floating rate note plus a swap from floating to fixed. Floating rate notes are always at par after coupon payments (ignoring credit risk...) so the pricing of a bond is the same as that of a swap. So the pricing of a callable bond is the same as that of a cancellable swap. A cancellable swap can be viewed as a swap minus the ...

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 ...

3

SEC tends to keep CUSIPS handy: http://www.sec.gov/divisions/investment/13flists.htm

3

One of the best pieces ever written on this topic is Salomon's "Principles of Principal Components," which is readily available on the Internet. I won't go into the details, since this paper is ridiculously comprehensive, but the fundamental idea is straightforward -- if you run a PCA based on yields, the first three components capture most of the variances, ...

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

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

If I understand correctly the question, you wish to completely hedge the interest rate risk (defined as a parallel shift in the yield curve). If that is the case, you should use modified duration, which is the price sensitivity, rather than the MacAulay duration. They are usually close in value, but not quite the same. Fortunately, you can easily transform ...

2

Unfortunately I don't think it's possible to compute returns purely based on yields... There are a few options: If you're on the buy side, you can easily get access to Barclay, Citi, or BofA's bond indices. These are very high quality datasets for studying historical bond returns. If you have Bloomberg, they've started providing bond indices as well. They ...

2

You're thinking of a "cross-currency basis swap", not a CCS. A CCS is a floating-for-floating swap that would, for example, let you switch 3m SHIBOR into 3m USD Libor. A cross-currency basis swap, on the other hand, is a swap of funding spreads (loosely speaking, LIBOR - OIS equivalent). It's essentially the liquid way of exchanging currency for long ...

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

It is a Wiener integral as your integrand is a deterministic function of time. It is known that the Wiener integral is stationary gaussian process with independent increments. So $z(t) \sim \mathcal N\left(0, \int_0^te^{-2k(t-s) }~ds\right)$ and $(z(t)-z(s)) \amalg z(u), \ \forall u,s,t \in \mathbb R_+ \text{ such that }u\leq s, s\leq t$ or alternatively ...

2

No, 9th character is computed using deterministic algorithm described here: http://en.wikipedia.org/wiki/CUSIP#Check_digit_pseudocode.

2

For a swap, we have a sequence of re-setting and payment dates. The # of forward rates corresponding to the # of payment dates. For example, let us assume that we have $n$ payment dates $t_1, \ldots, t_n$, where $0< t_1 < \cdots < t_n$. Then there are $n$ forward rates. During the simulation, for time steps prior to $t_1$, there exist $n$ ...

2

If the bond's DV01 is 0.05, then the DV01 of 1000 of this bond will be $0.05\times 1000 = 50$. By contrast, if the modified or effective duration of the bond is 0.05, then the modified duration of 1000 of this bond is still 0.05.

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 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

Under the Vasicek's model, the price of a zero-coupon bond is given by \begin{align*} P(t, T) = A(t, T)\exp\big(-B(t, T) r_t\big), \end{align*} where $A$ and $B$ are deterministic functions. In particular, $B$ is a positive increasing function (see any books on interest rate models). Then \begin{align*} \ln P(t, T) = \ln A(t, T) - B(t, T) r_t. \end{align*} ...

2

The Fed publishes yield curve data (par, zero & fwd) built with the Svensson model and using coupon bonds: http://www.federalreserve.gov/econresdata/researchdata/feds200628_1.html. The data is 2 day delayed, however.

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

If you just need the description you can use =BDP(TICKER,"CIE DES") directly in Excel.

2

Zero coupon rates are outputs, not inputs. As mentioned in the other post, given the parameters (say the initial guesses), you can easily compute the theoretical prices of each bond, which can then be converted into their theoretical yields (standard price to yield conversion). You should minimize the residuals between these theoretical yields and the market ...

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

I don't do TRI, so I may be wide of the mark, but: Euribor is not an instrument. It originated as a fixing to reflect the cost of borrowing for a term (here 3m) in the interbank market. But it is not an instrument, so there is no return to reinvest, nor an instrument to reinvest in. Instruments that do depend on 3m Euribor are FRAs, Futures, IRS, and then ...

1

It really depends on what you're trading on. Very often, butterfly trades are simply mean reverting trades. For example, you may look at 2s/5s/10s (typically on a regression or PCA-weighted basis) and see whether it's trading at "extreme" levels relative to history (i.e., are 5s trading rich or cheap relative to where 2s and 10s are trading). This can be ...

1

Given that you have swap rates and Cap prices (ATM, I assume), you can back out the IVs for the time periods using by bootstrapping. Strictly speaking, you would need Caplet prices for the given strikes. In such a case, You would look at the shortest dated cap and (assume) it is made up of only one caplet. You can then use black's formula and back out ...

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