# Tag Info

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To explain why a negative sloping yield curve is bad, you have to start with a theory of the yield curve. The dominant theories for the term structure of interest rates are the rational expectations, liquidity preference, and market segmentation. (The first two theories are quite compatible with each other and have more standing so let's assume that view.) ...

5

I like to present to you a slightly different approach: Historically, only one single yield curve was derived from different instruments, such as OIS, deposit rates, or swap rates. However, market practice nowadays is to derive multiple swap curves, optimally one for each rate tenor. This idea goes against the idea of one fully-consistent zero coupon curve, ...

5

The Macaulay duration is a measure of how sensitive a bond's price is to changes in interest rates. Duration is related to, but differs from, the slope of the plot of bond price against yield-to-maturity. The slope of the price-yield curve is $-\frac{D}{1+r}P,$ where $D$ is Macaulay duration, $P$ is bond price, and $r$ is yield. Here's how the definition ...

5

The short answer is that Libor swap rates come from the market. They represent a series of cashflows in the future whose value is determined by the fixing, which the market participants have their own valuations of. Since the actual cash flows are now discounted using a separate funding curve, the swap prices embed both a prediction of future fixings and a ...

4

The answer to your first four questions is affirmative. Option-adjusting the spread makes an equivalence between everything theoretically possible, but the quality of results depends significantly on the quality of your interest rate model and its calibration. My personal opinion, though, is that the results need to be treated carefully because the OAS ...

3

The original Nelson Siegel paper describes a parsimonious model of the term structure using only four or three (if $\lambda_t$ is fixed). Filipovic (1999) proves that this model can never be used in a arbitrage free context, paraphrasing the abstract: We introduce the class of consistent state space processes, which have the property to provide an ...

3

The risk implied by Euribor or EONIA (or their swaps) is for lending to another prime rated bank. These rate indexes represent where contributor banks are offering funds to each other in the interbank market. Contributing banks are mostly rated P-1 (Moody’s) or A-1 (S&P). You wouldn’t use these rates for govt discount curves because the risk doesn’t ...

3

You should use the full yield curve, discounting cash flows at specific dates using the appropriate zero-coupon interest rate. As to which yield curve, that is often a matter of convention. Generally one uses the LIBOR/swaps curve for all but the most liquid products (in which case you use the treasury curve). The curve is constructed from LIBOR/Eurodollar ...

3

Standard 3m curve interpretation: H, M, U, Z = Mar, Jun, Sep, Dec IMM dates in the futures convention (see SRKX's answer), and 2Y would be just the calendar 2y point. Assuming that what you found was done in 11th July 2011: U1 21 Sep 11 - 21 Dec 11 (IMM = 3rd Wednesday to following IMM) Z1 21 Dec 11 - etc H2 21 Mar 12 M2 20 Jun 12 U2 19 Sep 12 Z2 ...

3

I think they are using the same convention as the future exchanges for delivery months. You can find a complete mapping on the wiki page. The letter corresponds to a month and the number corresponds to the last digit of the year. So for example to understand U1 you find U=>September and 1=>2011 (you have to "guess" the relevant decade, it's quite ...

3

You can create the data using the procedure described in the reference manual on pages 31 and 32. The necessary code is copied below: # The following code may be used to generate an empty data set, # which can then be filled with bond data: ISIN <- vector() MATURITYDATE <- vector() STARTDATE <- vector() COUPONRATE <- vector() PRICE <- ...

3

Theoretically, a rising yield curve is compensation for the additional duration risk. An inverted yield-curve is saying that the market thinks that: Next-year's figures for: growth plus inflation is less than Ten years' time's figures for: growth plus inflation Which means that expectations are either of a recession (some negative economic growth; and ...

2

The way you are trying to solve these equations makes assumptions about the rates less than 10 years and therefore the shape of the yield curve. \$90 is the value of 8% coupons plus a 10-year zero-coupon bond. \$80 is the value of the 4% coupons plus a 10-year zero-coupon bond. 8% coupons are worth twice 4% coupons over the same period, regardless of the ...

2

$dF(t,T)$ describes the dynamics of the rate of a particular forward contract as time $t$ moves forward to a fixed expiration $T$. $d\bar F(t,\tau)$ describes the dynamics of the rate at a particular point on the yield curve as time moves forward. The differential $\frac{\partial F}{\partial T}dt$ is simply the difference between holding the expiration ...

2

You are going to need to interpolate in some way shape or form.... Linear is the easiest and most basic, however it may not capture the curvature, you can use splines to better capture the curve. A nice guide to doing so is here: It's a guide to bootstrapping and it has all the components. http://www.business.mcmaster.ca/finance/deavesr/yieldcur.pdf

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Samuelson once quipped that the yield curve had successfully predicted 9 of the last 5 recessions. Explanations for why the yield curve inverts have been covered adequately above. But what does it mean for the economy? For the yield curve inversion to predict stock market performance enough to make an actual decision, the bond market would have to be more ...

2

An inverted yield curve basically means that interest rates will be higher for the coming year than for the years following. That means that entities that need do borrow for short term purposes will do so at a greater cost that those borrowing for the long term. That is an unusual and "unnatural" relationship. All other things being equal, that will dampen ...

2

You are correct: none of the durations are the slope of (the tangent to) the price/yield curve. Rather the slope is the "dollar duration" = modified duration * Price *-1. This will tend to betray rather large numbers; e.g., under continuous compounding the modified/Macaulay duration of a 100 par 10-year zero coupon bond is 10.0 years. The slope (of the ...

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To elaborate on Freddy's answer: These days you need to maintain a separate funding (usually OIS) curve to your Libor* type curves. Once you have this discounting curve, you can calculate from Libor instrument market data what the market estimations of that Libor are: 3m instruments like Interest Rate Futures, IRS with a 3m float leg, 3m FRAs can be used to ...

1

(In addition to the answers of Freddy and Phil H): With "modern" multi-curve setups: You have to distinguish between discount curves (which describe todays value of the a future fixed payoff (e.g. a zero coupon bond)) and forward curve, which describe the expectation (in a specific sense) of future interest rate fixings. Swaps pay LIBOR rates and are ...

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Not sure this includes all data but certainly interest rate swaps. I heard somewhere FED Saint Luis (or was it another office) actually offers an API into their public data center, but I cannot confirm that: http://research.stlouisfed.org/fred2/categories/32299

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Let $P(t,T)$ be the time-$t$ price of the zero-coupon bond expiring at $T$. The no-arbitrage condition forces: $$e^{-\int_0^tr_sds}P(t,T)=\mathbb{E}[e^{-\int_0^Tr_sds}|\mathcal{F_t}],$$ where $\mathcal{F_t}$ is the filtration of the Brownian motion up to time $t$. Note that the expression on the right is a martingale by the tower property of expectations, ...

1

The top reference for this topic is Risk Management: Approaches for Fixed Income Markets by Golub and Tilman. The main measures you will want to calculate for hedging the yield curve risks of a bond portfolio are the key rate durations. The wikipedia article gives a brief overview. If you have access to Lehman/Barclays data, they calculate key rate ...

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