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	Model Batesa	Zmienność lokalna (Dupire)	Wycena w mierze neutralnej względem ryzyka
Dziedzina	Finanse ilościowe	Finanse ilościowe	Finanse ilościowe
Rodzina	Regression model	Regression model	Regression model
Rok powstania	1996	1994	1979
Twórca	David S. Bates	Bruno Dupire	John Harrison and David Kreps
Typ	Equity/FX Model	Equity/FX Model	Fundamental Principle
Źródło pierwotne	Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies, 9(1), 69-107.	Dupire, B. (1994). Pricing with a smile. Risk Magazine, 7(1), 18-20.	Harrison, J. M., & Kreps, D. M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381-408.
Inne nazwy	SVJ Model, Jump Diffusion	Deterministic Volatility Function, DVF	Risk-Neutral Measure, Q-Measure
Pokrewne	4	4	4
Podsumowanie	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.	Dupire's local volatility model (1994) is a deterministic framework that extracts a term and strike-dependent volatility function from market option prices. Unlike constant volatility, local volatility perfectly fits the observed implied volatility smile and is implemented via finite difference methods for European and American option pricing.	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.