Richardson Extrapolation Techniques for the Pricing of American-Style Options

Chung, San‐Lin; Chang, Chuang-Chang; Stapleton, Richard C.

doi:10.2139/ssrn.313962

Cited by 19 publications

(19 citation statements)

References 21 publications

(30 reference statements)

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“…In particular, in the partial differential equation (5) the derivatives with respect to S are discretized using the standard (centered) three-point finite difference scheme, whereas the derivative with respect to τ are computed using the implicit Euler time-stepping, whose accuracy is enhanced (up to second-order) by Richardson extrapolation (see Chang et al [2007], Tavella and Randall [2000]). …”

Section: Numerical Resultsmentioning

confidence: 99%

Pricing American options under the constant elasticity of variance model: An extension of the method by Barone-Adesi and Whaley

Ballestra¹,

Cecere²

2015

Finance Research Letters

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Section: Numerical Resultsmentioning

confidence: 99%

Pricing American options under the constant elasticity of variance model: An extension of the method by Barone-Adesi and Whaley

Ballestra¹,

Cecere²

2015

Finance Research Letters

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“…where E 1 and E 2 are as defined previously, and E 3 is the value of a pseudo-American exchange option 11 that can be exercised at T / 3, 2T / 3, or at T. However, as noted by Omberg (1987) and more recently by Chang and Stapleton (2001), plausible situations may exist where a non-uniform convergence occurs for this approximation. Since the three time-points used to calculate E 3 (T / 3, 2T / 3, and T) do not coincide with the two time-points used to calculate E 2 (T / 2, and T), a sequence of values E 1 ≤ E 2 N E 3 may occur.…”

Section: A1 Increasing Estimation Accuracy By Increasing the Numbermentioning

confidence: 99%

“…In turn, this leads to a non-uniform convergence. 12 To overcome this problem, Chang and Stapleton (2001), build on the suggestion of Omberg to use the geometric sequence [1, 2, 4, 8, …] of time-points of exercise, instead of the arithmetic sequence [1, 2, 3, 4, …]. As a result, Chang and Stapleton (2001) propose the following approximation 13 :…”

Section: A1 Increasing Estimation Accuracy By Increasing the Numbermentioning

confidence: 99%

A modified finite-lived American exchange option methodology applied to real options valuation

Armada

Kryzanowski

Pereira

2007

Global Finance Journal

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“…Note that the subscript N t has been removed from U k (S, y) and Ψ k (S, y) to keep the notation simple. According to (39) …”

Section: Time Discretizationmentioning

confidence: 99%

The evaluation of American options in a stochastic volatility model with jumps: An efficient finite element approach

Ballestra

Sgarra

2010

Computers & Mathematics with Applications

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a b s t r a c tWe consider the problem of pricing American options in the framework of a well-known stochastic volatility model with jumps, the Bates model. According to this model the asset price is described by a jump-diffusion stochastic differential equation in which the jump term consists of a Lévy process of compound Poisson type, while the volatility is modeled as a CIR-type process correlated with the asset price. Pricing American options under the Bates model requires us to solve a partial integro-differential equation with the final condition and boundary conditions prescribed on a free boundary. In this paper a numerical method for solving such a problem is proposed. In particular, first of all, using a Richardson extrapolation technique, the problem is reduced to a problem with fixed boundary. Then the problem obtained is solved using an ad hoc finite element method which efficiently combines an implicit/explicit time stepping, an operator splitting technique, and a nonuniform mesh of right-angled triangles. Numerical experiments are presented showing that the option pricing algorithm developed in this paper is extremely accurate and fast. In particular it is significantly more efficient than other numerical methods that have recently been proposed for pricing American options under the Bates model.

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Richardson Extrapolation Techniques for the Pricing of American-Style Options

Cited by 19 publications

References 21 publications

Pricing American options under the constant elasticity of variance model: An extension of the method by Barone-Adesi and Whaley

Pricing American options under the constant elasticity of variance model: An extension of the method by Barone-Adesi and Whaley

A modified finite-lived American exchange option methodology applied to real options valuation

The evaluation of American options in a stochastic volatility model with jumps: An efficient finite element approach

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