An elementary introduction to stochastic interest rate modeling /
Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each ch...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hackensack, N.J. :
World Scientific,
2012.
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| Edition: | 2nd ed. |
| Series: | Advanced series on statistical science & applied probability ;
v. 16. |
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- 1. A review of stochastic calculus. 1. Brownian motion. 1.2. Stochastic integration. 1.3. Quadratic variation. 1.4. Ito's formula. 1.5. Exercises
- 2. A review of Black-Scholes pricing and hedging. 2.1. Call and put options. 2.2. Market model and portfolio. 2.3. PDE method. 2.4. The Girsanov theorem. 2.5. Martingale method. 2.6. Exercises
- 3. Short term interest rate models. 3.1. Mean-reverting models. 3.2. Constant Elasticity of Variance (CEV) models. 3.3. Time-dependent models. 3.4. Exercises
- 4. Pricing of zero-coupon bonds. 4.1. Definition and basic properties. 4.2. Absence of arbitrage and the Markov property. 4.3. Absence of arbitrage and the Martingale property. 4.4. PDE solution: probabilistic method. 4.5. PDE solution: analytical method. 4.6. Numerical simulations. 4.7. Exercises
- 5. Forward rate modeling. 5.1. Forward contracts. 5.2. Instantaneous forward rate. 5.3. Short rates. 5.4. Parametrization of forward rates. 5.5. Curve estimation. 5.6. Exercises
- 6. The Heath-Jarrow-Morton (HJM) model. 6.1. Restatement of objectives. 6.2. Forward Vasicek rates. 6.3. Spot forward rate dynamics. 6.4. The HJM condition. 6.5. Markov property of short rates. 6.6. The Hull-White model. 6.7. Exercises
- 7. The forward measure and derivative pricing. 7.1. Forward measure. 7.2. Dynamics under the forward measure. 7.3. Derivative pricing. 7.4. Inverse change of measure. 7.5. Exercises
- 8. Curve fitting and a two-factor model. 8.1. Curve fitting. 8.2. Deterministic shifts. 8.3. The correlation problem. 8.4. Two-factor model. 8.5. Exercises
- 9. A credit default model. 9.1. Survival probabilities. 9.2. Stochastic default. 9.3. Defaultable bonds. 9.4. Credit default swaps. 9.5. Exercises
- 10. Pricing of caps and swaptions on the LIBOR. 10.1. Pricing of caplets and caps. 10.2. Forward rate measure and tenor structure. 10.3. Swaps and swaptions. 10.4. The London InterBank Offered Rates (LIBOR) model. 10.5. Swap rates on the LIBOR market. 10.6. Forward swap measures. 10.7. Swaption pricing on the LIBOR market. 10.8. Exercises
- 11. The Brace-Gatarek-Musiela (BGM) model. 11.1. The BGM model. 11.2. Cap pricing. 11.3. Swaption pricing. 11.4. Calibration of the BGM model. 11.5. Exercises.
