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Option valuation in markets with finite liquidity under fractional CEV assets | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 2، شماره 2، اسفند 2022، صفحه 167-180 اصل مقاله (330.5 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2023.15191 | ||
| نویسندگان | ||
Azadeh Ghasemifard 1؛ Seddigheh Banihashemi2؛ Afshin Babaei  3
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| 1University of Mazandaran | ||
| 2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. | ||
| 3Faculty of Mathematical sciences, University of Mazandaran, Babolsar, Iran. | ||
| چکیده | ||
| The aim of this paper is to numerically price the European double barrier option by calculating the governing fractional Black-Scholes equation in illiquid markets. Incorporating the price impact into the underlying asset dynamic, which means that trading strategies affect the underlying price, we consider markets with finite liquidity. We survey both cases of first-order feedback and full feedback. Asset evolution satisfies a stochastic differential equation with fractional noise, which is more realistic in markets with statistical dependence. Moreover, the Sinc-collocation method is used to price the option. Numerical experiments show that the results highly correspond to our expectation of illiquid markets. | ||
| کلیدواژه‌ها | ||
| Option pricing؛ Iliquid market؛ Sinc collocation method؛ Price impact&lrm | ||
| مراجع | ||
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[1] N. H. Chan, C. T. Ng, Fractional constant elasticity of variance model, Lecture Notes-Monograph Series (2006) 149-164. [2] S. Rostek, R. Schobel, A note on the use of fractional brownian motion for nancial modeling, Economic Modelling 30 (2013) 30-35. [3] K. J. Glover, P. W. Duck, D. P. Newton, On nonlinear models of markets with nite liquidity: some cautionary notes, SIAM Journal on Applied Mathematics 70 (8) (2010) 32523271. [4] G. Jumarie, Stock exchange fractional dynamics de ned as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations, Insurance: Mathematics and Economics 42 (1) (2008) 271287. [5] S. Shari an, A. R. Soheili, A. Neisy, A Numerical solution for the new model of time fractional bond pricing: Using a multiquadric approximation method, Journal of Mathematics and Modeling in Finance, 2 (1) (2022), Doi.org/10.22054/jmmf.2022.68274.1056. [6] M. Rezaei, A. Yazdanian, A. Ashra , S. Mahmoudi, Numerical pricing based on fractional Black-Scholes equation with time-dependent parameters under the CEV model: Double barrier options, Computers & Mathematics with Applications 90 (2021) 104-111. [7] I. Podlubny, Fractional differential equations, mathematics in science and engineering (1999). [8] F. Stenger, Numerical metods based on sinc and analytic functions (1993). [9] H. Takahasi, M. Mori, Double exponential formulas for numerical integration, Publications of the Research Institute for Mathematical Sciences 9 (3) (1974) 721-741. [10] T. Okayama, T. Matsuo, M. Sugihara, Error estimates with explicit constants for sinc approximation, sinc quadrature and sinc inde nite integration, Numerische Mathematik 124(2) (2013) 361-394. [11] J. Lund, K. L. Bowers, Sinc methods for quadrature and differential equations, SIAM, (1992). [12] A. Babaei, H. Jafari, S. Banihashemi, A numerical scheme to solve a class of two-dimensional nonlinear time-fractional diffusion equations of distributed order, Engineering with Computers (2020) 1-13. | ||
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