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| Model rynku Libor× | Wycena w mierze neutralnej względem ryzyka× | |
|---|---|---|
| Dziedzina | Finanse ilościowe | Finanse ilościowe |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 1997 | 1979 |
| Twórca≠ | Alan Brace, Dariusz Gatarek, and Marek Musiela | John Harrison and David Kreps |
| Typ≠ | Interest Rate Model | Fundamental Principle |
| Źródło pierwotne≠ | Brace, A., Gatarek, D., & Musiela, M. (1997). The market model of interest rate dynamics. Mathematical Finance, 7(2), 127-155. DOI ↗ | Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408. DOI ↗ |
| Inne nazwy | BGM Model, LMM | Risk-Neutral Measure, Q-Measure |
| Pokrewne | 4 | 4 |
| Podsumowanie≠ | 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. | Risk-neutral valuation (1979) is the fundamental principle that derivative prices equal the expected payoff discounted at the risk-free rate, computed under a risk-neutral probability measure (Q-measure). This principle, formalized by Harrison and Kreps, eliminates the need to estimate risk premia and is the foundation of modern derivatives pricing. |
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