Numerical method for discrete double barrier option pricing with time-dependent parameters

Farnoosh, Rahman; Sobhani, Amirhossein; Rezazadeh, H. R.; Beheshti, Mohammad Hossein

doi:10.1016/j.camwa.2015.08.016

Cited by 22 publications

(13 citation statements)

References 11 publications

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“…It has been extensively used by options traders and is known to result in considerable growth in options trading due to its effectiveness and accuracy in predicting the options prices. More recently, some techniques have been proposed for numerically approximating the B-S model such as Farnoosh et al (2015Farnoosh et al ( , 2016Farnoosh et al ( , 2017, Golbabai and Mohebianfar (2017a, b), Golbabai et al (2012Golbabai et al ( , 2014, Rad et al (2015), Rashidinia and Jamalzadeh (2017a, b), and Sobhani and Milev (2018).…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market

2019

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The price variation of the correlated fractal transmission system is used to deduce the fractional Black-Scholes model that has an α-order time fractional derivative. The fractional Black-Scholes model is employed to price American or European call and put options on a stock paying on a non-dividend basis. Upon encountering fractional differential equations, the efficient and relatively reliable numerical schemes must be obtained for their solution due to fractional derivatives being non-local. The present paper is aimed at determining the numerical solution of the time fractional Black-Scholes model (TFBSM) with boundary conditions for a problem of European option pricing involved with the method of radial basis functions (RBFs), which is a truly meshfree scheme. The TFBSM is discretized in the temporal sense based on finite difference scheme of order O(δt 2−α) for 0 < α < 1 and approximated with the help of the RBF in the spatial derivative terms. In addition, the stability and convergence of the proposed method are theoretically proven. Numerical results illustrate the accuracy and efficiency of the presented technique which is examined in the present study.

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Section: Introductionmentioning

confidence: 99%

Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market

2019

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“…e most famous PDE in finance is the Black-Scholes (B-S) model, which is broadly adopted for option pricing. So far, studies have presented different approaches for finding the numerical solution of this model and its variation when the exact form does not exist [5][6][7][8][9][10][11][12][13]. By using tick-by-tick data, Cartea and del-Castillo-Negrete [14] found that the value of European-style options satisfies a FPDE containing a nonlocal operator in time-to-maturity known as the Caputo fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Novel ANN Method for Solving Ordinary and Time‐Fractional Black–Scholes Equation

Bajalan

2021

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The main aim of this study is to introduce a 2-layered artificial neural network (ANN) for solving the Black–Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed to change the model into a sequence of ordinary differential equations (ODE). Subsequently, each of these ODEs is solved with the aid of an ANN. Adam optimization is employed as the learning paradigm since it can add the foreknowledge of slowing down the process of optimization when getting close to the actual optimum solution. The model also takes advantage of fine-tuning for speeding up the process and domain mapping to confront the infinite domain issue. Finally, the accuracy, speed, and convergence of the method for solving several types of the Black–Scholes model are reported.

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“…Refs. [12][13][14] show that the pricing of derivatives under discrete sampling assumption is more complex than continuous sampling assumption. The results of variance swaps with discrete sampling are usually obtained based on the stochastic volatility model.…”

Section: Introductionmentioning

confidence: 99%

A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate

2021

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At present, the study concerning pricing variance swaps under CIR the (Cox–Ingersoll–Ross)–Heston hybrid model has achieved many results ; however, due to the instantaneous interest rate and instantaneous volatility in the model following the Feller square root process, only a semi-closed solution can be obtained by solving PDEs. This paper presents a simplified approach to price log-return variance swaps under the CIR–Heston hybrid model. Compared with Cao’s work, an important feature of our approach is that there is no need to solve complex PDEs; a closed-form solution is obtained by applying the martingale theory and Ito^’s lemma. The closed-form solution is significant because it can achieve accurate pricing and no longer takes time to adjust parameters by numerical method. Another significant feature of this paper is that the impact of sampling frequency on pricing formula is analyzed; then the closed-form solution can be extended to an approximate formula. The price curves of the closed-form solution and the approximate solution are presented by numerical simulation. When the sampling frequency is large enough, the two curves almost coincide, which means that our approximate formula is simple and reliable.

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Numerical method for discrete double barrier option pricing with time-dependent parameters

Cited by 22 publications

References 11 publications

Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market

Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market

Novel ANN Method for Solving Ordinary and Time‐Fractional Black–Scholes Equation

A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate

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