A Radial Basis Function-Generated Finite Difference Method to Evaluate Real Estate Index Options

Aimi, A., & Guardasoni, C. (2018). Collocation boundary element method for the pricing of geometric Asian options. Engineering Analysis with Boundary Elements,92, 90–100.

Andersen, L. B., Häger, D., Maberg, S., Næss, M. B., & Tungland, M. (2012). The financial crisis in an operational risk management context: A review of causes and influencing factors. Reliability Engineering and System Safety,105, 3–12.

Bayona, V., Moscoso, M., & Kindelan, M. (2011). Optimal constant shape parameter for multiquadric based RBF-FD method. Journal of Computational Physics,230(19), 7384–7399.

Bayona, V., Moscoso, M., & Kindelan, M. (2012). Optimal variable shape parameter for multiquadric based RBF-FD method. Journal of Computational Physics,231(6), 2466–2481.

Bragt, D., Francke, M. K., Singor, S. N., & Pelsser, A. (2015). Risk-neutral valuation of real estate derivatives. Journal of Derivatives,23(1), 89–110.

Brennan, M. J., & Schwartz, E. S. (1978). Finite difference methods and jump processes arising in the pricing of contingent claims: A synthesis. Journal of Financial and Quantitative Analysis,13(3), 461–474.

Buttimer, R. J., Jr., Kau, J. B., & Slawson, V. C., Jr. (1997). A model for pricing securities dependent upon a real estate index. Journal of Housing Economics,6(1), 16–30.

Cao, J., Qiu, Y., & Song, G. (2017). A compact finite difference scheme for variable order subdiffusion equation. Communications in Nonlinear Science and Numerical Simulation,48, 140–149.

Case, K. E., Shiller, R. J., & Weiss, A. N. (1993). Index-based futures and options markets in real estate. Journal of Portfolio Management,19(2), 83–92.

Cavoretto, R., & De Rossi, A. (2019). Adaptive meshless refinement schemes for RBF-PUM collocation. Applied Mathematics Letters,90, 131–138.

Company, R., Egorova, V., Jódar, L., & Vázquez, C. (2016). Finite difference methods for pricing American put option with rationality parameter: Numerical analysis and computing. Journal of Computational and Applied Mathematics,304(Supplement C), 1–17.

Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics,7(3), 229–263.

De Rossi, A., & Perracchione, E. (2017). Positive constrained approximation via RBF-based partition of unity method. Journal of Computational and Applied Mathematics,319, 338–351.

Dehghan, M., & Mohammadi, V. (2017). Comparison between two meshless methods based on collocation technique for the numerical solution of four-species tumor growth model. Communications in Nonlinear Science and Numerical Simulation,44, 204–219.

Düring, B., & Pitkin, A. (2019). High-order compact finite difference scheme for option pricing in stochastic volatility jump models. Journal of Computational and Applied Mathematics,355, 201–217.

Fabozzi, F. J., Shiller, R. J., & Tunaru, R. S. (2012). A pricing framework for real estate derivatives. European Financial Management,18(5), 762–789.

Fereshtian, A., Mollapourasl, R., & Avram, F. (2019). RBF approximation by partition of unity for valuation of options under exponential Lévy processes. Journal of Computational Science,32, 44–55.

Fisher, J. D. (2005). New strategies for commercial real estate investment and risk management. Journal of Portfolio Management,31(SPEC. ISS.), 154–161.

Fornberg, B., & Lehto, E. (2011). Stabilization of RBF-generated finite difference methods for convective PDEs. Journal of Computational Physics,230(6), 2270–2285.

Geltner, D., & Fisher, J. (2007). Pricing and index considerations in commercial real estate derivatives: Understanding the basics. Journal of Portfolio Management,33(SPEC. ISS.), 99–118.

Golbabai, A., Ahmadian, D., & Milev, M. (2012). Radial basis functions with application to finance: American put option under jump diffusion. Mathematical and Computer Modelling,55(3), 1354–1362.

Golbabai, A., & Mohebianfar, E. (2017). A new method for evaluating options based on multiquadric RBF-FD method. Applied Mathematics and Computation,308, 130–141.

Golbabai, A., & Nikan, O. (2019). A computational method based on the moving least-squares approach for pricing double barrier options in a time-fractional Black–Scholes model. Computational Economics,1, 1.

Haghi, M., Mollapourasl, R., & Vanmaele, M. (2018). An RBF-FD method for pricing American options under jump–diffusion models. Computers and Mathematics with Applications,76(10), 2434–2459.

He, X., & Wang, J. (2018). Pricing real estate index options by compactly supported radial-polynomial basis point interpolation. Journal of Computational and Applied Mathematics,333, 350–361.

Hon, Y. C. (2002). A quasi-radial basis functions method for American options pricing. Computers and Mathematics with Applications,43(3), 513–524.

Kalantari, R., & Shahmorad, S. (2019). A stable and convergent finite difference method for fractional Black–Scholes model of American put option pricing. Computational Economics,53(1), 191–205.

Kansa, E. J., & Hon, Y. C. (2000). Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations. Computers and Mathematics with Applications,39(7), 123–137.

Koffi, R. S., & Tambue, A. (2019). A fitted multi-point flux approximation method for pricing two options. Computational Economics. https://doi.org/10.1007/s10614-019-09906-x

Lax, P. D., & Richtmyer, R. D. (1956). Survey of the stability of linear finite difference equations. Communications on Pure and Applied Mathematics,9(2), 267–293.

Lee, M.-K. (2019). Pricing perpetual american lookback options under stochastic volatility. Computational Economics,53(3), 1265–1277.

Madi, S., Cherif Bouras, M., Haiour, M., & Stahel, A. (2018). Pricing of American options, using the Brennan–Schwartz algorithm based on finite elements. Applied Mathematics and Computation,339, 846–852.

Marcozzi, M. D., Choi, S., & Chen, C. S. (2001). On the use of boundary conditions for variational formulations arising in financial mathematics. Applied Mathematics and Computation,124(2), 197–214.

Mollapourasl, R., Fereshtian, A., Li, H., & Lu, X. (2018). RBF-PU method for pricing options under the jump–diffusion model with local volatility. Journal of Computational and Applied Mathematics,337, 98–118.

Mollapourasl, R., Fereshtian, A., & Vanmaele, M. (2019). Radial basis functions with partition of unity method for American options with stochastic volatility. Computational Economics,53(1), 259–287.

Rad, J. A., Höök, J., Larsson, E., & von Sydow, L. (2018). Forward deterministic pricing of options using Gaussian radial basis functions. Journal of Computational Science,24, 209–217.

Rad, J. A., Parand, K., & Ballestra, L. V. (2015). Pricing European and American options by radial basis point interpolation. Applied Mathematics and Computation,251(Supplement C), 363–377.

Roque, C. M. C., Cunha, D., Shu, C., & Ferreira, A. J. M. (2011). A local radial basis functions: Finite differences technique for the analysis of composite plates. Engineering Analysis with Boundary Elements,35(3), 363–374.

Rosinger, E. E. (2008). Gap in nonlinear equivalence for numerical methods for PDEs. arXiv:0806.4491v2 [math.GM].

Sarra, S. A. (2012). A local radial basis function method for advection–diffusion–reaction equations on complexly shaped domains. Applied Mathematics and Computation,218(19), 9853–9865.

Shankar, V. (2017). The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD. Journal of Computational Physics,342, 211–228.

Soleymani, F., Barfeie, M., & Haghani, F. K. (2018). Inverse multi-quadric RBF for computing the weights of FD method: Application to American options. Communications in Nonlinear Science and Numerical Simulation,64, 74–88.

Su, L. (2019). A radial basis function (RBF)-finite difference (FD) method for the backward heat conduction problem. Applied Mathematics and Computation,354, 232–247.

Tangman, D. Y., Gopaul, A., & Bhuruth, M. (2008). A fast high-order finite difference algorithm for pricing American options. Journal of Computational and Applied Mathematics,222(1), 17–29.

Wang, J. G., & Liu, G. R. (2002). On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Computer Methods in Applied Mechanics and Engineering,191(23–24), 2611–2630.

Wendland, H. (2005). Scattered data approximation. Cambridge: Cambridge University Press.

Wong, S. M., Hon, Y. C., & Golberg, M. A. (2002). Compactly supported radial basis functions for shallow water equations. Applied Mathematics and Computation,127(1), 79–101.

Wu, Z. (1995). Compactly supported positive definite radial functions. Advances in Computational Mathematics,4(1), 283.

Xiao, J. R. (2004). Local Heaviside weighted MLPG meshless method for two-dimensional solids using compactly supported radial basis functions. Computer Methods in Applied Mechanics and Engineering,193(1–2), 117–138.

Zou, D., & Gong, P. (2017). A lattice framework with smooth convergence for pricing real estate derivatives with stochastic interest rate. Journal of Real Estate Finance and Economics,55(2), 242–263.