Linganisha mbinu

	Volatilite ya Ndani (Dupire)	Uwekaji Bei wa Crank-Nicolson
Nyanja	Fedha za Kiidadi	Fedha za Kiidadi
Familia	Regression model	Machine learning
Mwaka wa asili	1994	1947
Mwanzilishi	Bruno Dupire	John Crank and Phyllis Nicolson
Aina	Equity/FX Model	PDE Solver
Chanzo asilia	Dupire, B. (1994). Pricing with a smile. Risk Magazine, 7(1), 18-20.	Crank, J., & Nicolson, P. (1947). A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Mathematical Proceedings of the Cambridge Philosophical Society, 43(1), 50-67.
Majina mbadala	Deterministic Volatility Function, DVF	CN Method, Implicit Finite Difference
Zinazohusiana	4	3
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 Crank-Nicolson method is a widely-used implicit finite difference scheme for solving PDEs in option pricing. It provides second-order accuracy in both space and time, unconditional stability, and can efficiently price derivatives with early exercise features (American options) or complex boundary conditions.