Reference Entry10.1002/9780470061602.EQF12009
Crank–Nicolson Scheme
Michael B. Giles
- 15 May 2010
2
TL;DR: In this paper, the Crank-Nicolson method for numerical solution of parabolic partial differential equations, its numerical properties and its application to the Black-Scholes equation are described.
read more
Abstract: We describe the Crank–Nicolson method for the numerical solution of parabolic partial differential equations, its numerical properties and its application to the Black–Scholes equation. We also present the Rannacher start-up procedure that is required to achieve second-order accuracy for the option value and its first and second derivatives, and discuss extensions to nonlinear and multifactor applications.
Keywords:
finite difference methods;
partial differential equation;
discretization;
numerical stability;
iterative solution;
Black–Scholes;
Crank–Nicolson;
Rannacher;
θ-scheme
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Analysis of Quantization Error in Financial Pricing via Finite Difference Methods
TL;DR: The error of a second order finite difference scheme for the one-dimensional convection-diffusion equation is studied and nonsmooth initial conditions commonly encountered in convection processes are considered.
4
•Dissertation
Mathematical models for vector-borne disease: effects of periodic environmental variations.
Pamela M. Moschini
- 23 Jan 2015
TL;DR: A very simple SIS/SIR model for a general vector-borne disease transmission considering constant population sizes over the season, where contact between the host and the vector responsible of the transmission is assumed to occur only during the summer of each year is proposed.
2
References
Difference Methods for Initial-Value Problems
Robert D. Richtmyer,K. W. Morton +1 more
Abstract: Keywords: equations : differentielles ; stabilite ; transport ; transfert de chaleur ; mecanique des : fluides ; ondes Reference Record created on 2005-11-18, modified on 2016-08-08
4.5K
A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type
J. Crank,P. Nicolson,D. R. Hartree +2 more
- 01 Jan 1947
TL;DR: In this paper, the authors present methods of evaluating numerical solutions of the non-linear partial differential equation to the boundary conditions A, k, q are known constants, where q is the rate of heat generation.
3.4K
Quadratic Convergence for Valuing American Options Using a Penalty Method
Peter Forsyth,Kenneth R. Vetzal +1 more
TL;DR: The convergence of a penalty method for solving the discrete regularized American option valuation problem is studied and it is observed that an implicit treatment of the American constraint does not converge quadratically if constant timesteps are used.
Convergence remedies for non-smooth payoffs in option pricing
TL;DR: In this article, three methods of dealing with discontinuities are discussed: averaging the initial data, shifting the grid, and a projection method, combined with a special timestepping method, high accuracy is achieved.
Numerical convergence properties of option pricing PDEs with uncertain volatility
TL;DR: In this paper, the authors prove the convergence of a particular iterative scheme for one factor uncertain volatility models and demonstrate how non-monotone discretization schemes (such as standard Crank-Nicolson timestepping) can converge to incorrect solutions.