Quadratic Convergence for Valuing American Options Using a Penalty Method

By Peter A. Forsyth, Kenneth R. Vetzal. SIAM Journal on Scientific Computing, 2001

334 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/f43b8823c7cfe5a4248d08ac25899df7f60360e9

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In Finance

1. Peter A. Forsyth
2. Kenneth R. Vetzal
3. Jari Toivanen
4. Samuli Ikonen
5. S. Clift
6. George Labahn
7. Abdul Khaliq
8. Rebecca Carter

Citations in the corpus

• Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation (2006, background): “Let V0 be the linear function satisfying the boundary conditions (9) defined by V0(x) = (1 − x/X)g(t) = (1 − x/X)K, (11)”
• Efficient numerical methods for pricing American options under stochastic volatility (2008, methodology): “For option pricing this approach has been considered in [1], [10], [17], for example.”
• COMPONENTWISE SPLITTING METHODS FOR PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY (2007, methodology): “For option pricing it has been employed in [12], [27], for example.”
• Two-factor convertible bonds valuation using the method of characteristics/finite elements (2003, methodology): “Moreover, Forsyth and Vetzal (2001) compared the eKciency and the accuracy of an implicit penalty method for valuing American-style options with the commonly used technique of handling the American constraint explicitly in the lattice methodologies and they found that the partial di=erential…”
• Adaptive θ-methods for pricing American options (2008, background): “Recent years have seen the development of several approaches for the valuation of American options (see, for example, [1,5,7,8,12,22,23]).”
• Convergence analysis of Crank-Nicolson and Rannacher time-marching (2006, result): “This contrasts slightly with the results of Forsyth and Vetzal [2] who found that for American options this variable timestep gives second order convergence for the option value, whereas the uniform timestep does not, probably due to its inadequate resolution of the initial behaviour of the exercise”
• Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals (2009, methodology): “This set of coupled PDEs is solved, working backward in time, using an iterative penalty scheme [20] to determine the value of the guarantee at each timestep.”
• Numerical solution of two asset jump diffusion models for option valuation (2008, methodology): “[53, 54, 19] to produce a similarly quadratically convergent method.”
• Valuation of Convertible Bonds With Credit Risk (2003, background): “1 While in principle this is an attractive framework, it is subject to the same criticisms that have been applied to the valuation of risky debt by Jarrow and Turnbull [1995]. That is, because the value of the firm is not a traded asset, parameter estimation is difficult.”
• GUARANTEED MINIMUM WITHDRAWAL BENEFIT IN VARIABLE ANNUITIES (2008, positive): “KEY WORDS: guaranteed minimum withdrawal benefit, variable annuities, singular stochastic control model, penalty approximation, optimal withdrawal policies”
• Penalty methods for the numerical solution of American multi-asset option problems (2008, background): “Please see Forsyth and Vetzal [10] for further information.”
• A FAST, STABLE AND ACCURATE NUMERICAL METHOD FOR THE BLACK–SCHOLES EQUATION OF AMERICAN OPTIONS (2008, methodology): “Alternatively, penalty and front– fixing methods were developed (e.g. in [17], [30]).”
• Pricing American Options Using LU Decomposition (2007, methodology): “For example, the widely used projected SOR method is applied for option pricing in [31], a penalty method in [10], and a front-fixing method in [24].”
• Using meshfree approximation for multi-asset American option problems (2004, methodology): “In [7] it was established that their penalty method applied together with a finite volume spatial discretization leads to a quadratically convergent numerical scheme.”
• Using meshfree approximation for multi‐asset American options (2004, background): “Forsyth and Vetzal (2002) established that their penalty method applied together with a finite volume spatial discretization leads to a quadratically convergent numerical scheme.”
• Finite-Horizon Optimal Investment with Transaction Costs: A Parabolic Double Obstacle Problem (2009, neutral): “[2], [7], [11] and [18]).”