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| Numerairumváltás× | Libor Piaci Modell× | |
|---|---|---|
| Tudományterület | Kvantitatív pénzügy | Kvantitatív pénzügy |
| Módszercsalád | Regression model | Regression model |
| Keletkezés éve≠ | 1995 | 1997 |
| Megalkotó≠ | Hélyette Geman, Nicole El Karoui, Jean-Charles Rochet | Alan Brace, Dariusz Gatarek, and Marek Musiela |
| Típus≠ | Measure Theory | Interest Rate Model |
| 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 ↗ | Brace, A., Gatarek, D., & Musiela, M. (1997). The market model of interest rate dynamics. Mathematical Finance, 7(2), 127-155. DOI ↗ |
| Alternatív nevek | Numeraire Switching, Measure Change | BGM Model, LMM |
| 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 LIBOR Market Model (BGM), developed by Brace, Gatarek, and Musiela (1997), is a multi-factor interest rate model that directly models forward LIBOR rates as lognormal processes. Unlike short-rate models, LMM naturally prices caplets at the market level and is the industry standard for valuing caps, floors, and exotic interest rate derivatives. |
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