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| HJM-Framework× | Änderung des Numeraires× | |
|---|---|---|
| Fachgebiet | Quantitative Finanzwirtschaft | Quantitative Finanzwirtschaft |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 1992 | 1995 |
| Urheber≠ | David Heath, Robert Jarrow, and Andrew Morton | Hélyette Geman, Nicole El Karoui, Jean-Charles Rochet |
| Typ≠ | Interest Rate Framework | Measure Theory |
| Wegweisende Quelle≠ | Heath, D., Jarrow, R. A., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60(1), 77-105. DOI ↗ | Geman, H., El Karoui, N., & Rochet, J. C. (1995). Changes of numeraire, changes of probability measure and option pricing. Journal of Applied Probability, 32(2), 443-458. DOI ↗ |
| Aliasnamen | Forward Rate Model, No-Arbitrage Drift Condition | Numeraire Switching, Measure Change |
| Verwandt≠ | 4 | 3 |
| Zusammenfassung≠ | The Heath-Jarrow-Morton (HJM) framework (1992) is a general no-arbitrage approach to modeling the entire term structure of forward rates. Unlike short-rate models, HJM works directly with forward rates f(t,T) and specifies their volatility; the drift is then determined by arbitrage constraints. This flexibility enables multi-factor modeling and accurate calibration to swaption matrices. | Change of numeraire is a mathematical technique for simplifying option pricing by changing the choice of discount factor (numeraire). By selecting a numeraire aligned with the payoff structure, complex problems become simple. The technique is essential for LIBOR market models and multi-currency derivatives. |
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