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| Uthamini Usio na Hatari (Risk-Neutral Valuation)× | Mabadiliko ya Numeraire× | |
|---|---|---|
| Nyanja | Fedha za Kiidadi | Fedha za Kiidadi |
| Familia | Regression model | Regression model |
| Mwaka wa asili≠ | 1979 | 1995 |
| Mwanzilishi≠ | John Harrison and David Kreps | Hélyette Geman, Nicole El Karoui, Jean-Charles Rochet |
| Aina≠ | Fundamental Principle | Measure Theory |
| Chanzo asilia≠ | Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408. 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 ↗ |
| Majina mbadala | Risk-Neutral Measure, Q-Measure | Numeraire Switching, Measure Change |
| Zinazohusiana≠ | 4 | 3 |
| Muhtasari≠ | 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. | 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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