Pricing American barrier options with discrete dividends by binomial trees

Gaudenzi, Marcellino; Zanette, Antonino

doi:10.1007/s10203-009-0089-4

Cited by 10 publications

(4 citation statements)

References 9 publications

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“…Later Cheuck-Vorst [3] present a modification of the trinomial method (based on a change of the geometry of the tree) which allows to set a layer of nodes exactly on the barrier for every choice of the number of time steps. Gaudenzi-Lepellere [8] introduce suitable interpolations of binomial values and Gaudenzi-Zanette [9] construct a tree where all the mesh points are generated by the barrier itself. However, all the previous methods are not able to price efficiently double barrier options.…”

Section: Introductionmentioning

confidence: 99%

The Binomial Interpolated Lattice Method for Step Double Barrier Options

Appolloni

Gaudenzi

Zanette

2014

Int. J. Theor. Appl. Finan.

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We consider the problem of pricing step double barrier options with binomial lattice methods. We introduce an algorithm, based on interpolation techniques, that is robust and efficient, that treats the "near barrier" problem for double barrier options and permits the valuation of step double barrier options with American features. We provide a complete convergence analysis of the proposed lattice algorithm in the European case.

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Section: Introductionmentioning

confidence: 99%

The Binomial Interpolated Lattice Method for Step Double Barrier Options

Appolloni

Gaudenzi

Zanette

2014

Int. J. Theor. Appl. Finan.

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“…Unfortunately, their approach can not be directly extended to price barrier stock options with discrete dividends. While Zvan et al (2000) and Gaudenzi and Zanette (2009) develop numerical methods to price barrier options under Model 3, to our knowledge, no announced papers derive analytical pricing formulae for pricing barrier stock options with discrete dividend payouts.…”

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confidence: 98%

Pricing barrier stock options with discrete dividends by approximating analytical formulae

Dai

Chiu

2013

Quantitative Finance

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Deriving accurate analytical formulas for pricing stock options with discrete dividend payouts is a hard problem even for the simplest vanilla options. This is because the falls in the stock price process due to discrete dividend payouts will significantly increase the mathematical difficulty in pricing the option. On the other hand, much literature uses other dividend settings to simplify the difficulty, but these settings may produce inconsistent pricing results. This paper derives accurate approximating formulae for pricing a popular path-dependent option, the barrier stock option, with discrete dividend payouts. The fall in stock price due to dividend payout at an exdividend date t is approximated by an accumulated price decrement due to a continuous dividend yield up to time t. Thus, the stock price process prior to time t and after time t can be separately modelled by two different lognormal-diffusive stock processes which help us to easily derive analytical pricing formulae. Numerical experiments suggest that our formulae provide more accurate and coherent pricing results than other approximation formulae. Our formulae are also robust under extreme cases, like the high volatility (of the stock price) case. Besides, our formulae also extend the applicability of the first-passage model (a type of structural credit risk model) to measure how the firm's payout influences its financial status and the credit qualities of other outstanding debts.

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“…In this section we will discuss the binomial tree that will be used for our pricing problems. We will use the approach introduced in [8] in order to treat efficiently the problem of the specification error on the barrier due to the binomial method (see [2]). …”

Section: Tree Structure For Barrier Optionsmentioning

confidence: 99%

“…This method, based on the idea to choose trees with a line of nodes closest as possible to the barrier, permits to obtain sufficiently precise estimates, but it is problematic in the case of a barrier closed to the initial value of the underlying asset ("near barrier problem"). Here we use the algorithm proposed in Gaudenzi-Zanette [8] in order to further increase the efficiency of the numerical procedures presented for the Parisian/ParAsian options. Such an algorithm is based on a backward procedure where the nodes of the tree are generated from the barrier and it permits to overcome the problem related to the specification error of the barrier (see Figlewsky-Gao [6]) and to treat the near barrier problem in a natural way.…”

Section: Introductionmentioning

confidence: 99%

Fast binomial procedures for pricing Parisian/ParAsian options

Gaudenzi

Zanette

2017

Comput Manag Sci

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The discrete procedures for pricing Parisian/ParAsian options depend, in general, by three dimensions: time, space, time spent over the barrier. Here we present some combinatorial and lattice procedures which reduce the computational complexity to second order. In the European case the reduction was already given by Lyuu-Wu [11] and , in this paper we present a more efficient procedure in the Parisian case and a different approach (again of order 2) in the ParAsian case. In the American case we present new procedures which decrease the complexity of the pricing problem for the Parisian/ParAsian knock-in options. The reduction of complexity for Parisian/ParAsian knock-out options is still an open problem.Key-words: Parisian options, ParAsian options, tree methods, binomial methods, combinatorial formulas * Dipartimento di Scienze Economiche e Statistiche, Via Tomadini 30/A, Università di Udine, 33100 Udine, Italy (E-mail: gaudenzi@uniud.it, antonino.zanette@uniud.it)Méthodes binomiales rapides pour le pricing d'options parisienne et parAsian Résumé :Les méthodes à temps discret pour le pricing des options parisienne et parAsian dépendent généralement de trois paramètres : Le temps, l'espace et le temps écoulé proche de la barrière.Dans ce travail, nous présentons des procédures combinatoires et de treillis qui permettent de réduire d'ordre 2 la complexité du calcul. Ces simplifications ont déjà été utilisées par Lyuu-Wu et Li-Zhao dans le cas des options européennes. Dans cet article, une technique plus efficace est employée pour les options parisienne et parAsian. Nous introduisons aussi de nouvelles méthodes rapides pour les options américaines applicables aux parisiennes et parAsians knock-in. La généralisation de ce type de procédures aux options parisienne/parAsian knock-out reste un problème ouvert.

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Pricing American barrier options with discrete dividends by binomial trees

Abstract: American options, Barrier options, Tree methods, Discrete dividends, Singular points, G13, C63,

Cited by 10 publications

References 9 publications

The Binomial Interpolated Lattice Method for Step Double Barrier Options

The Binomial Interpolated Lattice Method for Step Double Barrier Options

Pricing barrier stock options with discrete dividends by approximating analytical formulae

Fast binomial procedures for pricing Parisian/ParAsian options

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