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| Numerairumváltás× | HJM keretrendszer× | |
|---|---|---|
| Tudományterület | Kvantitatív pénzügy | Kvantitatív pénzügy |
| Módszercsalád | Regression model | Regression model |
| Keletkezés éve≠ | 1995 | 1992 |
| Megalkotó≠ | Hélyette Geman, Nicole El Karoui, Jean-Charles Rochet | David Heath, Robert Jarrow, and Andrew Morton |
| Típus≠ | Measure Theory | Interest Rate Framework |
| Alapmű≠ | 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 ↗ | 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 ↗ |
| Alternatív nevek | Numeraire Switching, Measure Change | Forward Rate Model, No-Arbitrage Drift Condition |
| Kapcsolódó≠ | 3 | 4 |
| Összefoglaló≠ | 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. | 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. |
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