Linganisha mbinu

	Volatilite ya Ndani (Dupire)	Modeli ya Bates
Nyanja	Fedha za Kiidadi	Fedha za Kiidadi
Familia	Regression model	Regression model
Mwaka wa asili	1994	1996
Mwanzilishi	Bruno Dupire	David S. Bates
Aina	Equity/FX Model	Equity/FX Model
Chanzo asilia	Dupire, B. (1994). Pricing with a smile. Risk Magazine, 7(1), 18-20.	Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies, 9(1), 69-107.
Majina mbadala	Deterministic Volatility Function, DVF	SVJ Model, Jump Diffusion
Zinazohusiana	4	4
Muhtasari	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.	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.