A numerical method to price discrete double Barrier options under a constant elasticity of variance model with jump diffusion

Ahmadian, Davood; Ballestra, Luca Vincenzo

doi:10.1080/00207160.2014.986114

Cited by 9 publications

(11 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, by substituting (17) in the second of relations (15) and by using, for S > S max , the approximation V(S, i ) ≃ Se −r d i − Ee −r i (consistently with the second of the boundary conditions [14], see, e.g., Kirkby 29 ), the remaining term I 2, i, j in (15) is computed as follows:…”

Section: Discretization Of the Integral Termmentioning

confidence: 99%

“…In fact, in order to apply the FFT algorithm, we should be able to transform the partial differential equation being solved into a partial differential equation with coefficients that do not vary with respect to the space variable (as happens for 63). For some option pricing models (such as the constant elasticity of variance model, see Hsu et al 46 and Ahmadian and Ballestra 15 ), this cannot be done.…”

Section: Problem 3: American Call Optionmentioning

confidence: 99%

“…Finally, as a possible future development, one could generalize the proposed numerical method to other option pricing models, such as the constant elasticity of variance jump‐diffusion model (see Ahmadian and Ballestra 15 ), or the fractional Brownian motion with jumps (see, e.g., Xiao et al 47 ).…”

Section: Conclusion and Future Developmentsmentioning

confidence: 99%

“…To this aim, both finite difference schemes (see, e.g., Khaliq et al, Wade et al, Andersen and Andreasen, Carr and Anita, Cont and Voltchkova, Patel and Mehra, and d'Halluin et al [7][8][9][10][11][12][13][14] and finite element methods (see, e.g., Ahmadian and Ballestra 15 and Feng and Linetsky 16 ) have been developed. However, when using these approaches, the presence of the integral term in the equation being solved leads to full linear systems, which, if the number of spatial discretization nodes is large, require a special numerical treatment.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An extremely efficient numerical method for pricing options in the Black–Scholes model with jumps

Ahmadian

Ballestra

Karimi

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

We propose a new numerical method for pricing options in the Black-Scholes model with jumps. Specifically, we consider the partial integro-differential problem that yields the option price, and we solve it by means of a finite difference scheme that combines a fixed-point iteration technique and a repeated space-time Richardson extrapolation procedure. Such an approach turns out to be not only extremely accurate and fast but also very simple to implement, since the use of fast convolution techniques for handling the jump integral is not required. Numerical experiments are presented in which vanilla, barrier, and American options are considered.

show abstract

Section: Discretization Of the Integral Termmentioning

confidence: 99%

Section: Problem 3: American Call Optionmentioning

confidence: 99%

Section: Conclusion and Future Developmentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An extremely efficient numerical method for pricing options in the Black–Scholes model with jumps

Ahmadian

Ballestra

Karimi

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…As traditional numerical algorithm performs badly in nonsmooth solutions, Golbabai, Ballestraand Ahmadian used finite element method (FEM) to improve orders of convergence in [9]. In [10], Ahmadian and Ballestra found it also performs well under a constant elasticity of variance model with jump diffusion. For some models, the other way to get numerical method is directly starting from the analytic solution.…”

Section: Introductionmentioning

confidence: 99%

Numerical Methods for Discrete Double Barrier Option Pricing Based on Merton Jump Diffusion Model

Li¹

2017

OJS

View full text Add to dashboard Cite

As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming. In the current studies, some scholars just obtained theoretical derivation, or gave some simulation calculations. Others impose underlying assets on some strong assumptions, for example, a lot of calculations are based on the Black-Scholes model. This thesis considers Merton jump diffusion model as the basic model to derive the pricing formula of discrete double barrier option; numerical calculation method is used to approximate the continuous convolution by calculating discrete convolution. Then we compare the results of theoretical calculation with simulation results by Monte Carlo method, to verify their efficiency and accuracy. By comparing the results of degeneration constant parameter model with the results of previous models we verified the calculation method is correct indirectly. Compared with the Monte Carlo simulation method, the numerical results are stable. Even if we assume the simulation results are accurate, the time consumed by the numerical method to achieve the same accuracy is much less than the Monte Carlo simulation method.

show abstract

The finite element method: A high‐performing approach for computing the probability of ruin and solving other ruin‐related problems

Ahmadian

Ballestra

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

The finite element method (FEM), despite being a very powerful tool for solving partial differential equations, has never been used to compute the probability of ruin, nor it has been applied to other kinds of ruin-related problems, at least to the best of our knowledge. In this paper, in order to explore possible applications of the FEM in insurance mathematics, a high-order FEM is proposed to solve problems related to ruin. Specifically, a FEM based on either quadratic, cubic, or quartic polynomials is developed to compute the probability of ruin and the (discounted) expected value of the assets of a firm in two previously published ruin models. Moreover, when dealing with the calculation of the probability of ruin, a suitable operator splitting technique is employed, such that the FEM variational formulation is used to approximate only spatial derivatives. Numerical experiments are presented showing that the FEM performs extraordinarily well. In fact, the solutions of the two problems considered can be obtained with an error (in the maximum norm) of order 10 −5 or even smaller in a time smaller than a second. Finally, in accordance with already established theoretical results, the FEM reveals to be superconvergent at the boundaries of the finite elements.

show abstract

A numerical method to price discrete double Barrier options under a constant elasticity of variance model with jump diffusion

Cited by 9 publications

References 61 publications

An extremely efficient numerical method for pricing options in the Black–Scholes model with jumps

An extremely efficient numerical method for pricing options in the Black–Scholes model with jumps

Numerical Methods for Discrete Double Barrier Option Pricing Based on Merton Jump Diffusion Model

The finite element method: A high‐performing approach for computing the probability of ruin and solving other ruin‐related problems

Contact Info

Product

Resources

About