A two-step simulation procedure to analyze the exercise features of American options

Basso, Antonella; Nardon, Martina; Pianca, Paolo

doi:10.1007/s10203-004-0045-2

Cited by 7 publications

(2 citation statements)

References 29 publications

(27 reference statements)

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“…In this section we shall describe briefly how to treat numerically the free boundary x f (τ ) in (2.4). For more details on the optimal exercise time we refer the reader to [7].…”

Section: Numerical Treatment Of the Free Boundarymentioning

confidence: 99%

A Fast, Stable and Accurate Numerical Method for the Black–scholes Equation of American Options

Ehrhardt

Mickens

2008

Int. J. Theor. Appl. Finan.

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In this work we improve the algorithm of Han and Wu [SIAM J. Numer. Anal. 41 (2003), 2081–2095] for American Options with respect to stability, accuracy and order of computational effort. We derive an exact discrete artificial boundary condition (ABC) for the Crank–Nicolson scheme for solving the Black–Scholes equation for the valuation of American options. To ensure stability and to avoid any numerical reflections we derive the ABC on a purely discrete level. Since the exact discrete ABC includes a convolution with respect to time with a weakly decaying kernel, its numerical evaluation becomes very costly for large-time simulations. As a remedy we construct approximate ABCs with a kernel having the form of a finite sum-of-exponentials, which can be evaluated in a very efficient recursion. We prove a simple stability criteria for the approximated artificial boundary conditions. Finally, we illustrate the efficiency and accuracy of the proposed method on several benchmark examples and compare it to previously obtained discretized ABCs of Mayfield and Han and Wu.

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“…In this section we shall describe briefly how to treat numerically the free boundary x f (τ ) in (2.4). For more details on the optimal exercise time we refer the reader to [7].…”

Section: Numerical Treatment Of the Free Boundarymentioning

confidence: 99%

A Fast, Stable and Accurate Numerical Method for the Black–scholes Equation of American Options

Ehrhardt

Mickens

2008

Int. J. Theor. Appl. Finan.

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“…This relatively small tweak implies that Curran's boundary theory can be relaxed to include a wider subset of parameter inputs for CRR. Basso et al (2002, 2004) developed a binomial approximation to the optimal exercise boundary with the insight of Kim–Byun boundary theory. Areal and Rodrigues (2013) extended Curran's boundary theory to accelerate the binomial lattice for valuing American options with discrete dividends.…”

Section: Introductionmentioning

confidence: 99%

American option pricing: Optimal Lattice models and multidimensional efficiency tests

Shang

Byrne

2020

Journal of Futures Markets

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We introduce a set of lattice techniques to the Leisen‐Reimer and Tian binomial models with a view to accelerating computation time and improving accuracy of American Option valuation. A level of accuracy and efficiency combined can be achieved that surpass commonly used analytical analogues. We compare these efficient lattice models with analytical formulae for pricing different groups of options according to the deepness of American quality and moneyness. Our results reveal that counter to received wisdom, lattices constructs produce greater speed and accuracy for all option categories relative to the best performing closed form American analogues.

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Binomial algorithms for the evaluation of options on stocks with fixed per share dividends

Nardon¹,

Pianca²

2010

Mathematical and Statistical Methods for Actuarial Sciences and Finance

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Stocks frequently pay dividends, which has implications for the value of options written on these assets. High dividends imply lower call premia and higher put premia. Recently, Haug et al. [13] derive an integral representation formula that can be considered the exact solution to problems of evaluating both European and American call options and European put options. For American-style put options it may be optimal to exercise at any time prior to expiration, even in the absence of dividends. In this case, numerical techniques, such as lattice approaches, are required. Discrete dividends produce discrete shift in the tree; as\ud a result, the tree is no longer reconnecting beyond any dividend date. While methods based on non-recombining trees give consistent results, they are computationally expensive, since at each node at an ex-dividend date and up to maturity a new binomial tree has to be generated and evaluated. In this contribution, we analyze binomial algorithms for the evaluation of options written on stocks which pay discrete dividends of both European and American type. We consider both algorithms which\ud force the reconnection of the binomial tree, without altering the structure of the dynamics of prices, and an algorithm which translates a continuous efficient approximation

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A two-step simulation procedure to analyze the exercise features of American options

Cited by 7 publications

References 29 publications

A Fast, Stable and Accurate Numerical Method for the Black–scholes Equation of American Options

A Fast, Stable and Accurate Numerical Method for the Black–scholes Equation of American Options

American option pricing: Optimal Lattice models and multidimensional efficiency tests

Binomial algorithms for the evaluation of options on stocks with fixed per share dividends

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