Option pricing in high volatile illiquid market

[1] D Bakstein and S. Howison, A non-arbitrage liquidity model with observable parameters
for derivatives (2003).
[2] G. Barles and H.M. Soner, Option pricing with transaction costs and a nonlinear BlackScholes equation, Finance and Stochastics 2, no. 4 (1998), pp. 369-397.
[3] F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of
political economy 81, no. 3 (1973), pp. 637-654.
[4] Z. Buckov ˇ a, M. Ehrhardt, M. G ´ unther and P. P ¨ olvora ´ , Alternating direction explicit
methods for linear, nonlinear and multi-dimensional Black-Scholes models, Novel Methods
in Computational Finance, (2017), 333-371.
[5] R. Company, E. Navarro, J. R. Pintos, and E. Ponsoda, Numerical solution of linear
and nonlinear blackscholes option pricing equations, Computers & Mathematics with Applications, 56(3) (2008), pp. 813821.
[6] G. Dibeh, and H. M. Harmanani, Option pricing during post-crash relaxation times, Physica A: Statistical Mechanics and its Applications, 380 (2007), pp. 357-365.
[7] B. During, C. Hendricks and J. Miles ¨ , Sparse grid high-order ADI scheme for option
pricing in stochastic volatility models, Novel Methods in Computational Finance, Springer,
Cham, (2017), pp. 295-312.
[8] M. Ehrhardt, Nonlinear models in mathematical finance: new research trends in option
pricing, Nova Science Publishers, 2008.
[9] Y. El-Khatib and A. Hatemi-J, Option pricing with illiquidity during a high volatile period,
Mathematical Methods in the Applied Sciences, 45(5),(2022), pp. 3213-3224.
[10] R. Frey and P. Pierre, Risk management for derivatives in illiquid markets: A simulation
study, Advances in finance and stochastics, Springer, Berlin, Heidelberg (2002), pp. 137-159.
[11] M. N. Koleva,Positivity preserving numerical method for non-linear Black-Scholes models, Numerical Analysis and Its Applications: 5th International Conference, Springer Berlin
Heidelberg, (2012), pp. 363-370.
[12] H. E. Leland, Option pricing and replication with transactions costs, The journal of finance
40(5) (1985), 1283-1301.
[13] D. C. Lesmana and S. Wang, An upwind finite difference method for a nonlinear blackscholes equation governing european option valuation under transaction costs, Applied Mathematics and Computation, 219(16) (2013), pp. 88118828.
[14] H. Liu and J. Yong, Option pricing with an illiquid underlying asset market, Journal of
Economic Dynamics and Control, 29(12) (2005), pp. 2125-2156.
[15] S. Mashayekhi and J. Hugger, Finite difference schemes for a nonlinear Black-Scholes
model with transaction cost and volatility risk, Acta Mathematica Universitatis Comenianae,
84(2) (2015), pp. 255-266.
[16] S. Mashayekhi,Alternating Direction Explicit Method for a Nonlinear Model in Finance,
Advances in Mathematical Finance and Applications, 6(4) (2021), pp. 1-23.
[17] R.C Merton,Theory of rational option pricing, The Bell Journal of economics and management science (1973), pp. 141-183.
[18] D. Sornette and F. Cuypers, Why stock markets crash: Critical events in complex financial systems, Physics Today, 57(3) (2004),pp. 78-79.