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| Uthamini Usio na Hatari (Risk-Neutral Valuation)× | Mfumo wa SABR× | |
|---|---|---|
| Nyanja | Fedha za Kiidadi | Fedha za Kiidadi |
| Familia | Regression model | Regression model |
| Mwaka wa asili≠ | 1979 | 2002 |
| Mwanzilishi≠ | John Harrison and David Kreps | Patrick S. Hagan |
| Aina≠ | Fundamental Principle | Interest Rate Model |
| 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 ↗ | Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing smile risk. Wilmott Magazine, 1, 84-108. link ↗ |
| Majina mbadala≠ | Risk-Neutral Measure, Q-Measure | Stochastic Volatility Model |
| Zinazohusiana | 4 | 4 |
| 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. | The SABR (Stochastic Alpha-Beta-Rho) model is a stochastic volatility framework introduced by Hagan et al. in 2002 for valuing interest rate derivatives. It captures the smile effect in implied volatility through correlated Brownian motions and has become industry standard for swaption and caplet pricing. |
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