Alternating Direction Explicit Method for a Nonlinear Model in Finance
Subject Areas : Financial Mathematics
1 - Department of Mathematics, Faculty of Sciences, Arak University, Arak 38156-8-8349, Iran
Keywords:
Abstract :
[1] Bakstein, D. and Howison, S., A Non-arbitrage Liquidity Model with Observable Parameters for Derivatives, 2003.
[2] Barles, G. and Soner, H. M., Option Pricing with Transaction Costs and a Nonlinear Black-Scholes Equation. Finance and Stochastics, 1998, 2(4), P. 369-397.
[3] Black, F. and Scholes, M., The Pricing of Options and Corporate Liabilities. Journal of political economy, 1973, 81(3), P. 637-654.
[4] Buckova, Z., Ehrhardt, M., Gunther, M., and Polvora, P., Alternating Direction Explicit Methods for Linear, Nonlinear and Multi-Dimensional Black-Scholes Models. Novel Methods in Computational Finance, Springer, 2017, P. 333-371.
[5] Company, R., Navarro, E., Pintos, J. R., and Ponsoda, E., Numerical Solution of Linear and Nonlinear Black-Scholes Option Pricing Equations. Computers & Mathematics with Applications, 2008, 56(3), P. 813-821.
[6] Dibachi, H., Behzadi, M.H., Izadikhah, M., Stochastic Modified MAJ Model for Measuring the Efficiency and Ranking of DMUs, Indian Journal of Science and Technology, 2015, 8(8), P. 1-7, Doi: 10.17485/ijst/2015/v8iS8/71505
[7] During, B., Hendricks, C., and Miles, J., Sparse Grid High-Order ADI Scheme for Option Pricing in Stochastic Volatility Models. Novel Methods in Computational Finance, Springer, 2017, P. 295-312.
[8] Ehrhardt, M., Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing. Nova Science Publishers, 2008.
[9] Frey, R. and Patie, P., Risk Management for Derivatives in Illiquid Markets: A simulation Study, In Advances in finance and stochastics, Springer, 2002, P. 137-159.
[10] Izadikhah, M., Azadi, M., Shokri Kahi, V., Farzipoor Saen, R., Developing a new chance constrained NDEA model to measure the performance of humanitarian supply chains, International Journal of Production Research, 2019, 57(3), P. 662-682, Doi: 10.1080/00207543.2018.1480840
[11] Jokar, H., Shamsaddini, K., Daneshi, V., Investigating the Effect of Investors' Behavior and Management on the Stock Returns: Evidence from Iran. Advances in Mathematical Finance and Applications, 2018, 3(3), P. 41-52. Doi: 10.22034/amfa.2018.544948
[12] Koleva, M. N., Positivity Preserving Numerical Method for Non-linear Black-Scholes Models. In International Conference on Numerical Analysis and Its Applications, Springer, 2012, P. 363-370.
[13] Kratka, M., No Mystery Behind the Smile. RISK-LONDON-RISK MAGAZINE LIMITED, 1998, 11, P. 67-71.
[14] Leland, H. E., Option Pricing and Replication with Transactions Costs. The journal of Finance, 1985, 40(5), P. 1283-1301.
[15] Lesmana, D. C. and Wang, S, An upwind Finite Difference Method for a Nonlinear Black-Scholes Equation Governing European Option Valuation under Transaction Costs. Applied Mathematics and Computation, 2013, 219(16), P. 8811-8828.
[16] Leung, S. and Osher, S., An Alternating Direction Explicit (ADE) Scheme for Time-Dependent Evolution Equations. Preprint UCLA June, 2005, 9, P. 2005.
[17] Liu, H. and Yong, J, Option Pricing with an Illiquid Underlying Asset Market. Journal of Economic Dynamics and Control, 2005, 29(12), P. 2125-2156.
[18] Mashayekhi, S. and Hugger, J, Finite Difference Schemes for a Nonlinear Black-Scholes Model with Transaction cost and Volatility risk. Acta Mathematica Universitatis Comenianae, 2015, 84(2), P.255-266.
[19] Merton, R. C., Theory of Rational Option Pricing, The Bell Journal of economics and management science. 1973, P.141-83.
[20] Parsa, B., Sarraf, F., Financial Statement Comparability and the Expected Crash Risk of Stock Prices. Advances in Mathematical Finance and Applications, 2018, 3(3), P. 77-93. Doi: 10.22034/amfa.2018.544951
[21] Piacsek, S. A. and Williams, G. P., Conservation Properties of Convection Difference Schemes, Journal of Computational Physics, 1970, 6(3), P. 392-405.
[22] Roberts, K. and Weiss, N., Convective Difference Schemes, Mathematics of Computation, 1966, 20(94), P. 272-299.
[23] Salehi, A., Mohammadi, S., Afshari, M., Impact of Institutional Ownership and Board Independence on the Relationship Between Excess Free Cash Flow and Earnings Management. Advances in Mathematical Finance and Applications, 2017, 2(3), P. 91-105. Doi: 10.22034/amfa.2017.533104
[24] Tone, K., Toloo, M., Izadikhah, M., A modified slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research, 2020, 287 (2), P. 560-571, Doi: 10.1016/j.ejor.2020.04.019.
[25] Towler, B. F. and Yang, R. Y., Numerical Stability of the Classical and the Modified Saul'yev's Finite Difference Methods. Computers & Chemical Engineering, 1978, 2(1), P. 45-51.