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21
votes
6answers
4k views

Why is an inverted yield curve a problem?

Immediately preceding the worst of the financial crisis, my professors all pointed out to me that the yield curve had inverted -- short-term yields were more risky than 20-year or 30-year Treasury ...
13
votes
2answers
818 views

Why isn't the Nelson-Siegel model arbitrage-free?

Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e. $$dX_t=\sigma dB_t-AX_tdt$$ and the spot interest rate evolves by the following equation: $$r_t=a+b\cdot X_t.$$ After solving for $X_t$ ...
9
votes
5answers
9k views

how to derive yield curve from interest rate swap?

According to some textbooks, to derive the yield curve, quote overnight to 1 week: rates from interbank money market deposit, 1 month to 1 year: LIBOR; 1 year to 7 years: Interest Rate Swap; 7 ...
8
votes
1answer
507 views

Musiela parameterization

I have a question regarding the proof of the Musiela parametrization for the dynamics of the forward rate curve. If $T$ is the maturity, $\tau=T-t$ is the time to maturity, and $dF(t,T)$ defines the ...
8
votes
1answer
501 views

Bond curve extrapolation

What are the best methods to extrapolate bond yields from an existing curve that doesn't extend quite this far? For example, how would one come about finding a theoretical bond yield for a 40 or 50 ...
6
votes
2answers
1k views

Is Duration really the slope of the Price-Yield curve?

When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve. But is that really right? Duration is (change in price) divided ...
6
votes
1answer
651 views

About Option Adjusted Spread, rate curves and bonds comparison

I have few questions about using OAS as a measure of risk: does OAS allow for comparison between bonds with and without embedded options (e.g. a callable bond against a plain vanilla one against a ...
6
votes
1answer
646 views

Where do swap rates and/or long-term forward rates come from?

I apologize if this is supposed to be obvious, but ... . Libor spot rates are quoted up to a year, beyond that one can use Eurodollar futures to continue to build the curve. Let's say up to 3 years. ...
6
votes
1answer
90 views

Looking for a pricing library supporting Mutli-curve Framework

I am looking for a builder of Yield curves by tenors (O/N, 1M, 3M, 6M, 12M) respect to a given discount curve based on multi-curve framework as described below : Interest-rate Modelling with Multiple ...
6
votes
1answer
373 views

How to build the short end of a zero coupon curve for non-core Eurozone countries?

I am in the process of building zero coupon curves for some countries in the Eurozone. I have the following data sets: Euribor and EONIA Swap rates Bond price and yields The bond prices (and thus ...
6
votes
0answers
205 views

Implied term structure from risky discount curve: does it make sense?

We know that, taken every discount curve, it's possible to calculate its forward rates according to our tenor preferences. We know also that it's actually possible to extract an implied term ...
5
votes
3answers
241 views

Deriving Interest Rates

I am trying to teach myself about interest rate swaps, how they are priced, etc... Easy enough - just comparing cash flows of fixed and floating rate bonds. However, what I'm struggling with is how ...
5
votes
2answers
366 views

Which interest rate should I use for the discount rate in real-world pricing?

Suppose I want to compute the time value of money (present value, future value, etc). I need to put an interest rate into the calculation. Which real world interest rate would best be used here, ...
5
votes
1answer
412 views

What are some simple algorithms for hedging vanilla bonds?

My team will soon be implementing an auto hedger for our bond trading desk which will be integrated tightly with our risk application and I am interested in researching how this may work. Any advice ...
4
votes
1answer
270 views

Yield curve fitting example in Wilmott on Quant Finance p.528

In Wilmott on Quantitative Finance Vol. 2, p. 528, Section 31.4.2, is given a power series expansion for a zero coupon bond $$Z(r,t;T)=1+a(r)(T-t)+b(r)(T-t)^2+c(r)(T-t)^3+\dots$$ then it says to ...
4
votes
1answer
2k views

Bootstrapping spot rates from treasury yield curve

I'm attempting to construct a spot rate and forward rate curve from the 2011 daily treasury yield curve rates provided by the US Treasury. All US Treasury securities (1m, 3m, 6m, 1y, 2y, 3y, 5y, 7y, ...
3
votes
2answers
251 views

Question on yield curve fitting from Wilmott on Quant Finance p.529

My last question is related. At the top of p. 529, it says, "From the Taylor series expansion for $Z$ we find that the yield to maturity is given by $$-\frac{log ...
3
votes
2answers
567 views

Using the termstrc package in R

I am attempting to use the function estim_nss from the termstrc package in R to find the spot curve from constant maturity rates published by the Fed. I am using this package because I will need to ...
3
votes
1answer
225 views

How to manage evaluation date changes in QuantLib while using ImpliedTermStructure Class

I will not attach the whole code 'cause it would be just a huge waste of space and it would be not useful for this question's purpose. What I am going to attach here is a snippet code and its output, ...
3
votes
1answer
107 views

Attributing the change in NII to Shift, Twist and Butterfly

The movement of the zero rate curves can be decomposed into a shift movement (the level of interest rates) and a twist movement (the slope of the curve) and butterfly (the curvature of the curve). If ...
3
votes
1answer
283 views

How does the 2-factor Hull White model propagate the forward rates curve?

I've been trying to get a grasp on some of the basics of interest rate modeling, and am looking to simulate rates using the 2 factor Hull White model, which I am aware offers a more realistic model of ...
3
votes
0answers
139 views

RQuantLib: any difference between FixedRateBond() and FixedRateBondPriceByYield() with flat term structure?

Please, consider the following functions from RQuantLib package: FixedRateBond() ...
3
votes
0answers
260 views

How does one estimate theta in the Ho-Lee model from a yield curve?

I have a yield curve constructed using linear interpolation with data points every 3-months for US treasuries. I would like to use that calibrate a Ho-Lee model, but I can't wrap my head around how ...
2
votes
3answers
120 views

What do these maturity codes mean?

In fitting a curve I found that people are using the following tenors: U1 Z1 H2 M2 U2 Z2 2Y Could you please let me know what exact time periods they stand for? Is there a web page describing ...
2
votes
1answer
397 views

How to sum interest rate curves in QuantLib

C++ code taken from Bonds.cpp and slightly amended: ...
2
votes
1answer
214 views

QuantLib error with qlPiecewiseYieldCurveData() on qlPiecewiseYieldCurve() with ZeroYield and ForwardRate

I'm using QuantLibXL to build a discount curve, a zero yield curve and a forward curve of the EURIBOR rate (QuantLibXL is downloadable here). I've built an object of class ...
2
votes
1answer
60 views

Comparison of multicurve calibration methods

It seems that there are mayor softwares around offering a multicurve framework based on bootstrap. I find this puzzling nowadays, given the distinct advantages of best-fit optimization methods and ...
2
votes
1answer
281 views

Calculating instantaneous forward rate from zero-coupon yield curve

I have a big dataset containing zero-coupon bond yields with different relative maturities. I fix a time horizon on my dataset and I want to calculate instantaneous forward rate. I'm going to write ...
2
votes
1answer
773 views

Calculate the “ten year zero rate” given two bonds with two prices

I have a little question and need some help with the notation. So, the question goes as follows: A bond with a maturity of ten years that pays annual coupons of 8% has a price of \$90. A bond with ...
2
votes
1answer
95 views

Economic indicators leading the yield curve

There is a lot of research on how the government yield curve can be used to predict the economy. The government yield curve is often seen as a leading indicator. But for which variables is the curve a ...
2
votes
0answers
96 views

Bond (yield curve) dynamics in the Forward-LIBOR-market-model

The standard Libor-Forward-Market-Models provides a way of modelling the evolution of forward rates in time. However the model does not seem to be well suited for the modelling of zero-bonds. But ...
2
votes
0answers
282 views

Yield Curve Volatility

Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds. Each yield curve has its slope and its curvature, and they obviously change ...
1
vote
1answer
170 views

Derivation of the Nelson-Siegel model and proof of arbitrage

1. I am looking for a derivation of the Nelson-Siegel model $y(m)=a+b\left( \frac{1-e^{-\lambda m}}{\lambda m}\right)+c\left( \frac{1-e^{-\lambda m}}{\lambda m} -e^{-\lambda m} \right)$ It is ...
1
vote
1answer
158 views

“Friendly” papers about maximum smoothness yield curve modelling

I'm currently looking to implement some version of the yield curve modeling techniques in the maximum smoothness framework. The papers I have found so far explains the theory pretty well, but I find ...
1
vote
1answer
67 views

Cost of Carry Bear Flattener

I was reading a report last week that “the carry on a 2s5s gilt curve flattener is negative to the tune of 10bp over 6 months” and I realised I have little understanding of this concept and ...
1
vote
1answer
191 views

Interpolating spot rates given intermittent coupon-bond prices.

I'm trying to bootstrap spot rates given coupon-paying bond data. To simplify my problem, assume we are working with only 3 given data, the price/coupon rate on semi-annual bonds maturing in 0.5, 1, ...
1
vote
1answer
38 views

Yield to Maturity

For a bond with market price $P_t$ and fixed payments $c_n$, I'm told the yield to maturity is given by the solution $Y$ to the equation $P_t=\sum_{n=1}^N c_n e^{-Y(t_n-t)}$. Firstly, I'm not great ...
1
vote
0answers
107 views

Why is “full” Yield Curve (term structure of interest rates) 3 component based?

I am trying to understand bond-valuation and construction of yield curve. I don't have any exposure to bootstrapping or what-so-ever as of now. So it's appreciated to have an example but not too ...
0
votes
1answer
310 views

Zero Curve Calculation for AUD, CAD (post LIBOR scandal)

In the end of May 2013 British Bankers Association (BBA) stopped publishing LIBOR rates for Australian and Canadian dollars in a light of recent scandals. LIBOR rates were essential for creating zero ...
0
votes
1answer
114 views

Bloomberg Zero Coupon Rates

As some of your may know from my other posts, I am working on a Dynamic Nelson Siegel (DNS) based relative value trading model. On simulated data (which satisfies all the assumptions) of the DNS it ...
0
votes
1answer
52 views

OIS discounting pre and post crises

I have a Dynamic Nelson Siegel (DNS) based rv model. I want to know if I can use pre and post-crises curves interchangeably in my calibration and out of sample testing. I.e. those without OIS ...
0
votes
1answer
533 views

Deriving the par-yield curve

Given for example 6 bond prices and their respective 6 cashflows over a time period of 6 years, I have managed to derive the zero-coupon yield curve using the bootstrap method. However, it got lost ...
0
votes
0answers
44 views

Why use the E-curve as an interest rate benchmark?

EDSF or Eurodollar synthetic forward curve is used as an interest rate benchmark. Why? When should I use the EDSF "E-curve"? Any references would be extremely helpful.
0
votes
0answers
26 views

Forward Yield curve for an arbitrary company

Let say I am analyzing a company XYZ. Credit rating for this company is BB. Now I need to have the 6-month forward Yield curve for this company. Can somebody help me how to find this information from ...