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Viser: Term-Structure Models - A Graduate Course

Term-Structure Models
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Term-Structure Models Vital Source e-bog

Damir Filipovic
(2009)
Springer Nature
498,00 kr.
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Term-Structure Models - A Graduate Course, 1. udgave

Term-Structure Models

A Graduate Course
Damir Filipovic
(2009)
Sprog: Engelsk
Springer Berlin / Heidelberg
840,00 kr.
Print on demand. Leveringstid vil være ca 2-3 uger.

Detaljer om varen

  • Vital Source searchable e-book (Fixed pages)
  • Udgiver: Springer Nature (Juli 2009)
  • ISBN: 9783540680154
Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.
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Detaljer om varen

  • 1. Udgave
  • Hardback: 200 sider
  • Udgiver: Springer Berlin / Heidelberg (August 2009)
  • ISBN: 9783540097266

Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk.

The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.

1 Introduction.- 2 Interest Rates and Related Contracts.-
2.1 Zero-Coupon Bonds.-
2.2 Interest Rates.-
2.2.1 Market Example: LIBOR.-
2.2.2 Simple vs. Continuous Compounding.-
2.2.3 Forward vs. Future Rates.-
2.3 Bank Account and Short Rates.-
2.4 Coupon Bonds, Swaps and Yields.-
2.4.1 Fixed Coupon Bonds.-
2.4.2 Floating Rate Notes.-
2.4.3 Interest Rate Swaps.-
2.4.4 Yield and Duration.-
2.5 Market Conventions.-
2.5.1 Day-count Conventions.-
2.5.2 Coupon Bonds.-
2.5.3 Accrued Interest, Clean Price and Dirty Price.-
2.5.4 Yield-to-Maturity.-
2.6 Caps and Floors.-
2.7 Swaptions.- 3 Statistics of the Yield Curve.-
3.1 Principal Component Analysis (PCA).-
3.2 PCA of the Yield Curve.-
3.3 Correlation.- 4 Estimating the Yield Curve.-
4.1 A Bootstrapping Example.-
4.2 General Case.-
4.2.1 Bond Markets.-
4.2.2 Money Markets.-
4.2.3 Problems.-
4.2.4 Parameterized Curve Families.- 5 Arbitrage Theory.-
5.1 Self-Financing Portfolios.-
5.1.1 Financial Market.-
5.1.2 Self-financing Portfolios.-
5.1.3 Numeraires.-
5.2 Arbitrage and Martingale Measures.-
5.2.1 Contingent Claims.-
5.2.2 Arbitrage.-
5.2.3 Martingale Measures.-
5.2.4 Market Price of Risk.-
5.2.5 Admissible Strategies.-
5.2.6 The Fundamental Theorem of Asset Pricing.-
5.3 Hedging and Pricing.-
5.3.1 Attainable Claims.-
5.3.2 Complete Markets.-
5.3.3 Pricing.-
5.3.4 State-price Density.- 6 Short Rate Models.- Generalities.-
6.2 Diffusion Short Rate Models.-
6.2.1 Examples.-
6.3 Inverting the Yield Curve.-
6.4 Affine Term Structures.-
6.5 Some Standard Models.-
6.5.1 Vasicek Model.-
6.5.2 Cox-Ingersoll-Ross Model.-
6.5.3 Dothan Model.-
6.5.4 Ho-Lee Model.-
6.5.5 Hull-White Model.- 7 HJM Methodology.- Forward Curve Movements.-
7.2 Absence of Arbitrage
.-
7.3 Short Rate Dynamics.-
7.4 Fubini's Theorem.-
7.5 Explosion of Lognormal Forward Rates.- 8 Forward Measures.-
8.1 T-Bond as Numeraire.-
8.2 An Expectation Hypothesis.-
8.3 Option Pricing in Gaussian HJM Models.-
8.4 Black-Scholes Model with Stochastic Short Rates.- 9Forwards and Futures.-
9.1 Forward Contracts.-
9.2 Futures Contracts.-
9.3 Interest Rate Futures.-
9.4 Forward vs. Futures in a Gaussian Setup.- 10 Consistent Term Structure Parameterizations.-
10.1 No-Arbitrage Condition.-
10.2 Affine Term Structures.-
10.3 Polynomial Term Structures.-
10.4 Exponential-Polynomial Families.-
10.4.1 Nelson{Siegel Family.-
10.2 Svensson Family.- 11 Affine Processes.-
11.1 Option Pricing in Affine Models.-
11.1.1 Vasicek Model.-
11.1.2 Cox-Ingersoll-Ross Model.- 12 Market Models.-
12.1 Models of Forward LIBOR Rates.-
12.1.1 Discrete-tenor Case.-
12.1.2 Continuous-tenor Case.- 13 Default Risk.-
13.1 Transition and Default Probabilities.-
13.1.1 Historical Method.-
13.1.2 Structural Approach.-
13.2 Intensity Based Method.-
13.2.1 Construction of Intensity Based Models.-
13.2.2 Computation of Default Probabilities.-
13.2.3 Pricing Default Risk.-
13.2.4 Measure Change.
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