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| Uthamini Usio na Hatari (Risk-Neutral Valuation)× | Modeli ya Bates× | |
|---|---|---|
| Nyanja | Fedha za Kiidadi | Fedha za Kiidadi |
| Familia | Regression model | Regression model |
| Mwaka wa asili≠ | 1979 | 1996 |
| Mwanzilishi≠ | John Harrison and David Kreps | David S. Bates |
| Aina≠ | Fundamental Principle | Equity/FX 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 ↗ | Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies, 9(1), 69-107. DOI ↗ |
| Majina mbadala | Risk-Neutral Measure, Q-Measure | SVJ Model, Jump Diffusion |
| 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 Bates model (1996) combines stochastic volatility and jump diffusion to capture both the volatility smile and the implied volatility skew observed in equity and currency option markets. It extends the Heston model by adding a Poisson jump component to returns, making it suitable for pricing options when sudden price moves are expected. |
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