Methoden vergleichen

	Crank-Nicolson-Preisbildung	Lokale Volatilität (Dupire)
Fachgebiet	Quantitative Finanzwirtschaft	Quantitative Finanzwirtschaft
Familie	Machine learning	Regression model
Entstehungsjahr	1947	1994
Urheber	John Crank and Phyllis Nicolson	Bruno Dupire
Typ	PDE Solver	Equity/FX Model
Wegweisende Quelle	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.	Dupire, B. (1994). Pricing with a smile. Risk Magazine, 7(1), 18-20.
Aliasnamen	CN Method, Implicit Finite Difference	Deterministic Volatility Function, DVF
Verwandt	3	4
Zusammenfassung	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.	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.