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My M.S thesis on Quantifying the Interest Risk of Bonds by Simulation.

Chapters include: Intro. to bonds and risk in bond investments; Intro. to interest rate models (equilibrium, no arbitrage models).

Short rate simulation, parameter estimation (MLE), bond pricing and risk simulation principles are explained in detail for Vasicek, CIR, Hull-White, CIR++ and Two Factor Vasicek (both no-arbitrage and equilibrium) models.

Empirical comparison of these models for quantifying the risk is made using US, German and Canadian bond market data.

Çağatay Dağıstan.
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Historical US, German and Canadian yield data in R.

After download, open the "R" file and enter "ls()" command to see the data.

Çağatay Dağıstan.
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These notes by Dr. Richard C. Stapleton are excellent!
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thesis by A. d
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Thesis by Christa Cuchiero
The aim of this diploma thesis is to present the theory as well as the practical applications of affine interest rate models. On the basis of the general theory established by Duffie and Kan, we put emphasis on affine models whose state variables have - in contrast to their theoretical abstract definition - a reasonable economic interpretation. Starting from the very first term structure models, namely the Vasicek and the Cox-Ingersoll-Ross model, we describe in sequel two- and more-factor models that have appeared in literature. By means of the Vasicek model we exemplify the calibration to market yields as well as to market cap volatilities. However, our main focus are affine yield factor models developed by Duffie and Kan, which allow to relate the state variables to yields with different maturities. We show how to calibrate a two-factor version of this model to market data. The results are promising since the model fits the market yields from different dates very well while the parameters remain nearly constant
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Found in "Essays on Financial Econometrics" by Kees Evert Bouwman
1 Introduction 1
2 Arbitrage-Free Modeling of the Term Structure
3 A Unified Approach to Mean-Variance Portfolio Selection 49
4 Arbitrage Smoothing in Fitting a Sequence of Yield Curves 85
5 Modeling Asset Volatility with GARCH Models in the Presence of Out-liers 97
6 A Parsimonious Arbitrage-Free Model of the US Term Structure 129

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by Monika Piazzesi
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by Jianqing Fan, Jiancheng Jiang, Chunming Zhang and Zhenwei Zhou
Abstract: In an effort to capture the time variation on the instantaneous return and volatility functions, a family of time-dependent diffusion processes is introduced to model the term structure dynamics. This allows one to examine how the instantaneous return and price volatility change over time and price level. Nonparametric techniques, based on kernel regression, are used to estimate the time-varying coefficient functions in the drift and diffusion. The newly proposed semiparametric model includes most of the well-known short-term interest rate models, such as those proposed by Cox, Ingersoll and Ross (1985) and Chan, Karolyi, Longstaff and Sanders (1992). It can be used to test the goodness-of-fit of these famous time-homogeneous short rate models. The newly proposed method complements the time-homogeneous nonparametric estimation techniques of Stanton (1997) and Fan and Yao (1998), and is shown through simulations to truly capture the heteroscedasticity and time-inhomogeneous structure in volatility. A family of new statistics is introduced to test whether the time-homogeneous models adequately fit interest rates for certain periods of the economy. We illustrate the new methods by using weekly three-month treasury bill data.
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lecture notes by Damir Filipovic
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Lecture notes by Claus Munk

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"Optimal Hedging Strategy for Minimum Guarantees in Life Insurance Policies" by Yan Sun

Title not directly related to fixed income, but has good material with example matlab code to do LMM simulation, do PCA, etc.
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Instructors: Andrew Lesniewski and Leif Andersen

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by Jesper Lund
Slides from the lectures
February 3, Introduction and Bond Market Basics
February 10, Estimation of the Term Structure, Part I
February 17, Estimation of the Term Structure, Part II
February 24, Introduction to Risk-Neutral Pricing and Binomial Models
March 3, Risk-Neutral Pricing and Binomial Models (part II)
March 24, Term-Structure Models in Continuous Time (one-factor models)
March 31, Term-Structure Models in Continuous Time, Part II
April 14, Term-Structure Models in Continuous Time, Part III (multi-factor models)
April 21, Term-Structure Models in Continuous Time, Part IV (calibration, HJM)
April 23, Calibration in Binomial Models
April 28, Calibration in lattice models -- part II
May 5, Pricing Term-Structure Derivatives
May 12, Mortgage-Backed Securities
May 19, MBS (part II) and Risk-Management Issues

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article by Alexander Levin
Intensive developments in interest rate modeling have delivered a bold but confusing model selection choice to financial engineers, risk managers, and investment analysts. Do these modeling issues sound familiar?

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ch. 10 of Brigo, Damiano book - Interest rate models - theory and practice.
I was able to save it, hope this link stays there..
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by yacine ait-sahalia

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by Nicolas Privault
Stochastic interest rate models
MA6627 - Semester A, 2007/2008.
1. A review of stochastic calculus.
2. A review of Black-Scholes pricing.
3. Short term interest rate modelling.
4. Pricing of zero coupon bonds.
5. Forward rate modelling.
6. The Heath-Jarrow-Morton (HJM) model.
7. The forward measure and derivative pricing.
8. Curve fitting and a two factor model.
9. Pricing of caps and swaptions on the LIBOR.
10. The Brace-Gatarek-Musiela (BGM) model.
11. Appendix: Mathematical tools.


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by YELIZ YOLCU
The uncertainty attached to future movements of interest rates is an essential part of the Financial Decision Theory and requires an awareness of the stochastic movement of these rates. Several approaches have been proposed for modeling the one-factor short rate models where some lead to arbitrage-free term structures. However, no denite consensus has been reached with regard to the best approach for interest rate modeling. In this work, we brie y examine the existing one-factor interest rate models and estimate the parameters of Vasicek and Hull-White (Extended Vasi Models by using Turkey's term structure. Moreover, a trinomial interest rate tree is constructed to represent the evolution of Turkey's zero coupon rates.


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by Lane Hughston
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lecture notes by Pierre Collin-Dufresne
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book by Claus Munk

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by Wu, Chao-Sheng.

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by Andrew Ang and Michael Sherris

This paper surveys the main concepts and techniques of recent developments in the modeling of the term structure of interest rates that are used in the risk management and valuation of interest-rate-dependent cash flows. These developments extend the concepts of immunization and matching to a stochastic interest rate environment. Such cash flows include the cash flows on assets such as bonds and mortgage-backed securities as well as those for annuity products, life insurance products with interest-rate-sensitive withdrawals, accrued liabilities for definedbenefit pension funds, and property and casualty liability cash flows

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Thesis by Alexandra Urbanova Csajkova

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by Rolf Poulsen
Introduction 1
How to Read This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
How to Avoid Reading This Thesis . . . . . . . . . . . . . . . . . . . . . . 1
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Summaries of the Papers in the Thesis . . . . . . . . . . . . . . . . . . . . 2
2 Mathematical Finance 5
2.1 General Denitions and Results for Modelling Continuous Financial
Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The Black-ScholesModel . . . . . . . . . . . . . . . . . . . . . . . . . 8
Excursion; 8+ B-S proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Fixed Income Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 The Indirect Approach . . . . . . . . . . . . . . . . . . . . . . 16
Excursion; Non-linear Drift . . . . . . . . . . . . . . . . . . . . . . . 21
Excursion; JumpingMean . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.2 The Direct Approach . . . . . . . . . . . . . . . . . . . . . . . 33
Excursion; Simulation and Approximation Quality in Lognormal LIBORModels
. . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Re
ections on Fixed Income Modelling . . . . . . . . . . . . . . . . . . . . 46
3 Estimation of Discretely Observed Diusion Processes 48
3.1 General Denitions and Results . . . . . . . . . . . . . . . . . . . . . 49
Excursion; Density Approximation . . . . . . . . . . . . . . . . . . . . . . 50
Excursion; AML Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Excursion; Estimation of Short RateModels . . . . . . . . . . . . . . . . . 58
4 Conclusion 61
4.1 What's New? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 What's Next? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
References 64
Manuscripts 73
Paper I: Eight Valuation Methods in Financial Mathematics: The Black-Scholes
Formula as an Example, 30 pages
Paper II: A simple regime switching term structure model, 28 pages
Paper III: Stability of Derivative Prices in Market Models, 30 pages
Paper IV: A Comparison of Approximation Techniques for Transition Densities of
Diusion Processes, 57 pages
Paper V: Approximate Maximum Likelihood Estimation of Discretely Observed
Diusion Processes, 33 pages
Paper VI: Optimal Martingale and Likelihood Methods for Models of the Short
Rate of Interest, With Monte Carlo Evidence for the CKLS Specication and Applications
to Non-Linear Drift Models, 46 pages
Paper VII: Should He Stay or Should He Go? Estimating the Eect of Sacking
the Manager in Association Football, 8 pages
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69 page notes by Damir Filipovi
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by Raquel Medeiros Gaspar
This thesis consists of two papers that study forward price term structure models.
Forward prices differ from futures prices in stochastic interest rate settings and become in their own right an interesting object of study.
Forward prices with different maturities are martingales under different forward measures. This
mathematical property makes the term structure of forward prices always connected with the
term structure of bond prices, and this dependence makes forward price terms structure models relatively harder to handle.
For finite dimensional factor models, the first paper (Chapter 1) studies general quadratic
term structures.
These term structures include as special cases the affine term structures and the Gaussian
quadratic term structures, previously studied in the literature. We show, however, that there
are other, non-Gaussian, quadratic term structures and derive sufficient conditions for the existence of these general quadratic term structures for bond, futures and forward prices.
We exploit the connection with the term structure of bond prices and show that even in
quadratic short rate settings we can have affine term structures for forward prices.
Finally, we show how the study of futures prices is naturally embedded in a study of forward
prices, that the difference between the two prices has to do with the correlation between bond
prices and the price process of the underlying to the forward contract and that this difference
may be deterministic in some (non-trivial) stochastic interest rate settings.
In the second paper (Chapter 2) we study a fairly general Wiener driven model for the term
structure of forward prices.
The model, under a fixed martingale measure, Q, is described by using two infinite dimensional
stochastic differential equations (SDEs). The first system is a standard HJM model for (forward)
interest rates, driven by a multidimensional Wiener process W. The second system is an infinite
SDE for the term structure of forward prices on some specified underlying asset driven by the
same W. Since the zero coupon bond volatilities will enter into the drift part of the SDE for
these forward prices, the interest rate system is needed as input into the forward price system.
Given this setup we use the Lie algebra methodology of Bj
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by Yacine Aijt-Sahalia and Robert Kimmel
We develop and implement a technique for maximum likelihood estimation in closed-form of multivariate
a
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Quoted :
"
Andrew CAIRNS
tel: (+44) 131 451 3245
fax: (+44) 131 451 3249
e-mail: A. Cairns@ma.hw.ac.uk
Solutions to selected problems in my book can be found by looking at the following files. The tutorials (from my MSc lecture course) contain various problems which appear in the book, so users will need to match tutorial problems up with those in the book.
Andrew Cairns "



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Andrew Angy
Geert Bekaertz
We examine the econometric performance of regime switching models for interest rate data from the US, Germany and the UK. Regime switching models forecast better out-of-sample than single regime models, including an affine multi-factor model, but do not always match moments very well. Regime switching models incorporating international short rate and term spread information forecast better, match sample moments better, and classify regimes better than univariate regime switching models. Finally, the regimes in interest rates correspond reasonably well with business cycles, at least in the US.

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Roger Lord

Contents
�� Problem definition
�� The Black-Scholes case
�� Pricing with characteristic functions
�� Basket options in general models
�� Swaptions in affine L
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Schrager, D.F. and Pelsser A.A.J
We propose an approach to find an approximate price of a swaption in Affine Term Structure Models. Our approach is based on the derivation of approximate dynamics in which the volatility of the Forward Swap Rate is itself an affine function of the factors. Hence we remain in the Affine framework and well known results on transforms and transform inversion can be used to obtain swaption prices in ways similar to bond options (i.e. caplets). We demonstrate that we can also obtain a closed form formula for the approximate price which is based on square-root dynamics for the swap rate. The latter approximation is extremely fast while remaining accurate. The method can be easily generalized to price options on coupon bonds. Computational time compares favorably with other approximation methods. Numerical results on the quality of the approximation are excellent. Our results show that in Affine models, analogously to the LIBOR Market Model, LIBOR and Swap rates are driven by approximately the same type of (in this case affine) dynamics
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Charlotte Christiansen
The Aarhus School of Business, Denmark
Abstract: The paper aims to improve the knowledge of the empirical properties of the long maturity region of the forward rate curve. Firstly, the theoretical negative correlation between the slope at the long end of the forward rate curve and the term structure variance is recovered empirically and found to be statistically significant. Secondly, the expectations hypothesis is analyzed for the long maturity region of the forward rate curve using
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By Pouyan Mashayekh Ahangarani1
ABSTRACT A variety of continuous time series models of the short term riskless rate are estimated using Maximum Likelihood method on discretized models. Then the best model will be found that can fit the data better. A number of well-known models perform poorly in the comparison. Indirect Inference method is used for the best model in order to obtain consistent estimates. At the end, an empirical application of the stochastic model for interest rates will be used for pricing the call options of Nokia Company.

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by Xinfu Chen

4.1.5 Spot Rate, Forward Rate, and Implied Forward Rate . . . . . . . . . . . . . . . . . 107
4.1.6 Term Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.1.7 Forward and Futures Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.2 The Heath, Jarrow & Morton Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.2.1 The SDE for Bond Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.2.2 The Forward Rate Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.2.3 The Spot Rate Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.2.4 The Market Price of Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2.6 Real World vs. Risk
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by Chan, Karolyi, Longstaff and Sanders (CKLS)
Abstract
We estimate and compare a variety of continuous-time models of the short-term riskless rate using the Generalized Method of Moments. We find that the most successful models in capturing the dynamics of the short-term interest rate are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rate. A number of well-known models perform poorly in the comparisons because of their implicit restrictions on term structure volatility. We show that these results have important implications for the use of different term structure models in valuing interest rate contingent claims and in hedging interest rate risk.
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Slides on Fixed Income Models

Also there is one more slide for crash course on fixed income models
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