Questions tagged [yield-curve]

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24
votes
2answers
49k 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 ...
1
vote
1answer
2k views

Setting input parameters for Nelson Siegel Svensson model

I am trying to determine the parameters for the Nelson Siegel Svensson model and am solving a Non-Linear Optimization problem to do this. I am trying to solve: $$ \min_\theta{\sum{(p_i - \hat p_i)^2}...
8
votes
2answers
7k views

Best method for interpolating yield curve? [Multiple questions]

I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run ...
10
votes
3answers
2k 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 ...
3
votes
1answer
278 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 ...
24
votes
6answers
46k 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 ...
22
votes
2answers
2k 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 $X_t$ ...
8
votes
1answer
2k 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. ...
4
votes
1answer
3k views

QuantLib Python Swap Yield Curve Bootstrapping Dates and Maturities

This is somewhat related to the question I asked here but simpler. I am trying to bootstrap a yield curve from swaps, and am having a problem with the dates/maturities that are coming out. The code ...
3
votes
3answers
223 views

PCA for Risk bucketing

I'm working on a project to justify the use the certain tenors (2y, 5y, 10y, 30y) for risk bucketing. I'm a little stuck after calculating the principal components. Just to describe my approach- a) ...
2
votes
0answers
136 views

Monetary Policy and the Yield Curve PART ONE

As I understand it, the Fed has 3 tools for moving interest rates to combat inflation/unemployment: the discount rate, Fed Funds rate and open market operations. I'm trying to understand how the ...
8
votes
1answer
1k 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 ...
4
votes
2answers
2k 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 ...
4
votes
1answer
551 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
222 views

Monetary Policy and the Yield Curve PART TWO

The Fed has a number of tools/targets with which they manage monetary policy. I'm looking to refine a concise summary of them and looking for guidance/correction/validation. Think I understand these ...
1
vote
1answer
5k 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.
4
votes
1answer
1k 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 ...
3
votes
1answer
1k views

How to sum interest rate curves in QuantLib

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

Accrual in Default Derivation of Credit CDS Curve

In Trading Credit Curves Part I by JP Morgan we have that each point on a credit (CDS) curve represents: $$PV(\text{Fee Leg}) = PV(\text{Contingent Leg})$$ which is $$S_n \sum_{i=1}^{n}\Delta_i ...
2
votes
1answer
258 views

Why we should specify the evaluation date when using Quantlib yield curve? And why updating the evaluation Date is time consuming

I was runing some tests using the yield curve structure in quantlib mainly: PiecewiseYieldCurve It seems that I have to fix the evaluation date using such a line : Settings::instance().evaluationDate(...
1
vote
2answers
592 views

Principal component analysis for yield curve

I have Treasury yield data across 11 maturities for past 1 year. I have used a code in MATLAB for PCA on change in yield curve. Now, I have covariance matrix of daily/monthly yield curve changes, ...
1
vote
1answer
861 views

Applications of PCA to yield curve analysis

One of the applications of Principal Component Analysis in Finance is to analyse the shape of the yield curve. But what conclusions can be drawn exactly from performing this exercise? Does it help us ...
0
votes
1answer
738 views

QL-Python Bootstrapping Yield Curve FuturesRateHelper throwing off results

I'm trying to perform a bootstrap of a yield curve from deposit rates, futures, and swaps, and the interpolation is "blowing up" for the futures maturities being off by two orders of magnitude (100x). ...
0
votes
1answer
5k views

Stub rate and first fixing in IRS

I have 2 questions that probably are related. Suppose there is an IRS that pays a 2% fixed rate every 6 months and receives the Libor 3 months (but paid every 6 months). The swap starts today (March ...