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21
votes
6answers
7k 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
975 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 $X_t$ ...
10
votes
5answers
16k 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 ...
9
votes
1answer
757 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 ...
8
votes
1answer
748 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 ...
7
votes
2answers
188 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
2answers
2k 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
908 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
879 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
469 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
277 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
429 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
430 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
485 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
344 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
221 views

How can an inverted yield curve in a liquid market exist?

Take a liquid market like US T-bills, notes and bonds... Who would want a long-term security that yielded less than the short? Even if someone is a long-term lender, why wouldn't they hold the ...
3
votes
2answers
298 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
128 views

Basic LIBOR curve question

I'm new to the quant finance and have a very basic question about LIBOR curve. LIBOR is published every day for 4 different tenors (1M, 3M, 6M, 1Y), and each rate means how much annual interest ...
3
votes
1answer
651 views

How to sum interest rate curves in QuantLib

C++ code taken from Bonds.cpp and slightly amended: ...
3
votes
2answers
262 views

What is the yield on an infinitely lived ZCB?

I guess the price of a Zero-Coupon Bond with infinite maturity should go to zero, what about its yield? I am asking this because I was dealing with the yield curve and its asymptotic properties when ...
3
votes
2answers
766 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
2k 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 ...
3
votes
1answer
429 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
185 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
413 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
2answers
163 views

IR Yield Curve and Fixing Dates

Consider two FRAs. 3x6 , Effective 3 months from now, terminates in 6 months. The floating leg payer pays 3-month LIBOR. Fixing date for LIBOR 40 business days. To price this at par, the fixed leg ...
3
votes
0answers
161 views

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

Please, consider the following functions from RQuantLib package: FixedRateBond() ...
3
votes
0answers
333 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
2answers
5k views

What is the Swap Curve?

What is the so-called Swap Curve, and how does it relate to the Zero Curve (or spot yield curve)? Does it only refer to a curve of swap rates versus maturities found in the market? Or is it a swap ...
2
votes
3answers
132 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
365 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
138 views

Does Nelson-Siegel require adjustments to yield curve input data?

I am attempting to gain a better understanding of the limitations of the Nelson-Siegel model as described in Estimating the Yield Curve Using the Nelson-Siegel Model. As I have been playing around ...
2
votes
2answers
574 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 ...
2
votes
1answer
193 views

Pricing a bond contract from the yield curve

When giving a particular class in financial mathematics for a student I saw a problem in a list of exercises that says: How to calculate the price at 15 December 2010 of a bond paying a coupon of ...
2
votes
1answer
535 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 ...
2
votes
1answer
148 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
1k 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
181 views

Forecast 3m LIBOR USD. Budget purpose

How can I calculate/budget/find a expectation for the 3 month LIBOR for the next 3monts-4 years? I am calculating a CF scenario on USD 3month Libor + margin. With swaps and fixed rate this is easy, ...
2
votes
1answer
91 views

Building curves using onshore or offshore JPY overnight rates?

I am trying to build Japanese Yen interest rate curves. When defining the curve instruments for the 'OIS' (discount) curve (aka TONAR), I am uncertain as to which rate to use for the overnight deposit ...
2
votes
1answer
106 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
207 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
405 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
42 views

Arbitraging upward sloping yield curve

I read from various sources that yield curve is normally upward sloping. If that's the case, if we borrow short term and lend long term, won't we always make money on average? Let's say 1-year ...
1
vote
2answers
394 views

Bootstrap yield curve with QLNet / Quantlib

I am trying to grasp QLNet (C# version of Quantlib, all the functions of Quantlib have the same name and work the same way, so if you just know Quantlib, you can still help me), especially for pricing ...
1
vote
2answers
154 views

Who determine Sport rate curve (Yield Curve)

My study was in a Mathematical modelling, we studied much about theory, equations, how to resolve equation, how to implement, but we don't understand well where these equations come from. My ...
1
vote
1answer
265 views

Par and Zero Coupon Yield Curves

The government par yield curve shows a marginally lower yield than the Government zero coupon curve. What is the reason for this in general.
1
vote
1answer
255 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
219 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
102 views

What is a Basis Swap Curve?

I know what a Swap Curve is. But I don't understand what a Basis Swap Curve is and how it is constructed? Need some guidance on this.