Binomial options pricing has no closed-form solution

Georgiadis, Evangelos

doi:10.3233/af-2011-003

Cited by 5 publications

(2 citation statements)

References 8 publications

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“…Although pricing and hedging in the CRR model can be extended to time-dependent parameters, see e.g. § 11.4 in Privault (2009), the corresponding option pricing formulas have exponential instead of polynomial complexity, see also Georgiadis (2011).…”

Section: Introductionmentioning

confidence: 99%

A q-binomial extension of the CRR asset pricing model

Breton¹,

El-Khatib²,

Fan³

et al. 2021

Preprint

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We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on q-binomial (or Kemp) random walks, with application to default with logistic failure rates. This model allows us to consider time-dependent switching probabilities varying according to a trend parameter, and it includes tilt and stretch parameters that control increment sizes. Option pricing formulas are written using q-binomial coefficients, and we study the convergence of this model to a Black-Scholes type formula in continuous time. A convergence rate of order O(1/N ) is obtained when the tilt and stretch parameters are set equal to one.

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Section: Introductionmentioning

confidence: 99%

A q-binomial extension of the CRR asset pricing model

Breton¹,

El-Khatib²,

Fan³

et al. 2021

Preprint

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show abstract

“…Gerbessiotis [8] gave a parallel binomial option pricing method with independent architecture, studied algorithm parameter adjustment method of achieving the optimal theory acceleration, and verified the feasibility and effectiveness of the algorithm under different parallel computing environments. Georgiadis [9] tested that there is no so-called closed-form solution when pricing options with binary tree method. Simonato [10] posed Johnson binary tree based on the approximation to Johnson distribution of the random distribution, overcoming some possible problems in Edgeworth binary tree that the combination of skewness and kurtosis cannot constitute qualified random distribution.…”

Section: Introductionmentioning

confidence: 99%

Randomized Binomial Tree and Pricing of American-Style Options

Cao

2014

Mathematical Problems in Engineering

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Randomized binomial tree and methods for pricing American options were studied. Firstly, both the completeness and the no-arbitrage conditions in the randomized binomial tree market were proved. Secondly, the description of the node was given, and the cubic polynomial relationship between the number of nodes and the time steps was also obtained. Then, the characteristics of paths and storage structure of the randomized binomial tree were depicted. Then, the procedure and method for pricing American-style options were given in a random binomial tree market. Finally, a numerical example pricing the American option was illustrated, and the sensitivity analysis of parameter was carried out. The results show that the impact of the occurrence probability of the random binomial tree environment on American option prices is very significant. With the traditional complete market characteristics of random binary and a stronger ability to describe, at the same time, maintaining a computational feasibility, randomized binomial tree is a kind of promising method for pricing financial derivatives.

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Pricing options of security portfolio in cyclical economic environment

Mao

Wen

2019

J Asset Manag

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Binomial options pricing has no closed-form solution

Cited by 5 publications

References 8 publications

A q-binomial extension of the CRR asset pricing model

A q-binomial extension of the CRR asset pricing model

Randomized Binomial Tree and Pricing of American-Style Options

Pricing options of security portfolio in cyclical economic environment

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