Numerical convergence properties of option pricing PDEs with uncertain volatility

By D. Pooley, Peter A. Forsyth, Kenneth R. Vetzal. 2003

172 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/c6433720b684fd5e7bdc78f834478ff66a09383a

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Citations in the corpus

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE (2012, background): “It is worth insisting on the fact that if the scheme is not monotone, it may fail to converge to the correct solution (see [34] for an example)! We present the theory rather informally and we refer to the original articles for more details.”
Analysis of a penalty method for pricing a guaranteed minimum withdrawal benefit (GMWB) (2012, unknown): “We use240 central differencing as much as possible in the W direction to ensure that the positive coefficient241 condition is satisfied (see Pooley et al. (2003))242 αni,j ≥ 0 ; βni,j ≥ 0 .”
Numerical solution of two asset jump diffusion models for option valuation (2008, background): “Variable grid spacing [44] or time stepping [54] can provide computational savings, but this study does not investigate these issues.”
Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation (2010, unknown): “In (Pooley et al., 2003), examples were given in which seemingly reasonable discretizations of nonlinear option pricing PDEs were unstable or converged to the incorrect solution.”
Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance (2007, methodology): “We give a brief outline of the steps in this proof, and refer readers to [38] for details.”
Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals (2009, background): “In Pooley et al. (2003), the authors demonstrate how some reasonable discretization schemes either never converge or converge to a wrong solution.”
Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem (2012, unknown): “We consider the optimal harvesting decision and land value assuming 21See Pooley et al. (2003).”
Robust numerical methods for contingent claims under jump diffusion processes (2005, background): “A variety of exotic and path-dependent contracts can be handled in a straightforward way, and nonlinear models such as transaction costs or uncertain parameters (Pooley et al., 2003) can also be easily extended to the jump diffusion case.”
Convergence analysis of Crank-Nicolson and Rannacher time-marching (2006, methodology): “This solution, often referred to as Rannacher time-stepping, has been used with success in approximations of the Black-Scholes equations [6, 5, 12, 4, 7].”
Numerical Methods for Nonlinear PDEs in Finance (2012, background): “In [25], examples were given in which seemingly reasonable discretizations of nonlinear option pricing PDEs were either unstable or converged to the incorrect solution.”