Application of the local radial basis function-based finite difference method for pricing American options

References

• I. Boztosuna and A. Charafi, An analysis of the linear advection-diffusion equation using mesh-free and mesh- dependent methods, Eng. Anal. Boundary Elem. 26 (2002), pp. 889–895. doi: 10.1016/S0955-7997(02)00053-X
   Web of Science ®Google Scholar
• G. Chandhini and V.S.S.Y. Sanyasiraju, Local RBF-FD solutions for steady convection–diffusion problems, Int. J. Numer. Methods Eng. 72 (2007), pp. 352–378. doi: 10.1002/nme.2024
   Web of Science ®Google Scholar
• A.H.D. Cheng, M.A. Golberg, E.J. Kansa, and G. Zammito, Exponential convergence and h-c multiquadratic collocation method for partial differential equations, Numer. Methods Partial Diff. Equ. 19 (2003), pp. 571–594. doi: 10.1002/num.10062
   Web of Science ®Google Scholar
• P.P. Chinchapatnam, K. Djidjeli, and P.B. Nair, Unsymmetric and symmetric schemes for the unsteady convection diffusion equation, Comput. Methods Appl. Mech. Eng. 195 (2006), pp. 2432–2453. doi: 10.1016/j.cma.2005.05.015
   Web of Science ®Google Scholar
• S.L. Chung, M.W. Hung, and J.Y. Wang, Tight bounds on American option prices, J. Bank. Financ. 34 (2010), pp. 77–89. doi: 10.1016/j.jbankfin.2009.07.004
   Web of Science ®Google Scholar
• O. Davydov and D.T. Oanh, On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation, Comput. Math. Appl. 62 (2011), pp. 2143–2161. doi: 10.1016/j.camwa.2011.06.037
   Web of Science ®Google Scholar
• G.E. Fasshauer, A.Q.M. Khaliq, and D.A. Voss, Using meshfree approximation for multi-asset American options, J. Chinese Inst. Eng. 27 (2004), pp. 563–571. doi: 10.1080/02533839.2004.9670904
   Web of Science ®Google Scholar
• B. Fornberg and G. Wright, Stable computation of multiquadric interpolants for all values of shape parameter, Comput. Math. Appl 48 (2004), pp. 853–867. doi: 10.1016/j.camwa.2003.08.010
   Web of Science ®Google Scholar
• B. Fornberg, G. Wright, and E. Larsson, Some observation regarding interpolants in the limit of flate radial basis function, Comput. Math. Appl. 47 (2004), pp. 37–55. doi: 10.1016/S0898-1221(04)90004-1
   Web of Science ®Google Scholar
• B. Fornberg, E. Larsson, and N. Flyer, Stable computations with Gaussian radial basis functions, SIAM J. Sci. Comput. 33 (2011), pp. 869–892. doi: 10.1137/09076756X
   Web of Science ®Google Scholar
• B. Fornberg, E. Lehto, and C. Powell, Stable calculation of Gaussian-based RBF-FD stencils, Comput. Math. Appl. 65 (2013), pp. 627–637. doi: 10.1016/j.camwa.2012.11.006
   Web of Science ®Google Scholar
• A. Golbabai, D. Ahmadian, and M. Milev, Radial basis function with application to finance: American put option under jump diffusion, Math. Comput. Model. 55 (2012), pp. 1354–1362. doi: 10.1016/j.mcm.2011.10.014
   Web of Science ®Google Scholar
• Y.C. Hon, A quasi radial basis functions method for American option pricing, Comput. Math. Appl. 43 (2002), pp. 513–524. doi: 10.1016/S0898-1221(01)00302-9
   Web of Science ®Google Scholar
• Y.C. Hon and X.Z. Mao, A radial basis function method for solving option price models, Financ. Eng. 8 (1999), pp. 31–49.
   Google Scholar
• J.C. Hull, Options, Futures, and Other Derivatives, 4th ed., Prentice–Hall, Upper Saddle River, NJ, 2000.
   Google Scholar
• S. Ikonen and J. Toivanen, Operator splitting methods for American option pricing, Appl. Math. Lett. 17 (2004), pp. 809–814. doi: 10.1016/j.aml.2004.06.010
   Web of Science ®Google Scholar
• N. Ju, Pricing an American option by approximating its early exercise boundary as multipiece exponential function, Rev. Financ. Stud. 11 (2003), pp. 627–646. doi: 10.1093/rfs/11.3.627
   Web of Science ®Google Scholar
• M.K. Kadalbajoo, L.P. Tripathi, and A. Kumar, A cubic B-spline collocation method for a numerical solution of the generalized Black–Scholes equation, Math. Comput. Model. 55 (2012), pp. 1483–1505. doi: 10.1016/j.mcm.2011.10.040
   Web of Science ®Google Scholar
• M.K. Kadalbajoo, A. Kumar, and L.P. Tripathi, Application of radial basis function with L-stable Padé time marching scheme for pricing exotic option, Comput. Math. Appl. 66 (2013), pp. 500–511. doi: 10.1016/j.camwa.2013.06.002
   Web of Science ®Google Scholar
• A.Q.M. Khaliq, D.A. Voss, and S.H.K. Kazmi, A linearly implicit predictor–corrector scheme for pricing American options using a penalty method approach, J. Bank. Financ. 30 (2006), pp. 489–502. doi: 10.1016/j.jbankfin.2005.04.017
   Web of Science ®Google Scholar
• A.Q.M. Khaliq, D.A. Voss, and S.H.K. Kazmi, Adaptive θ−methods for pricing American options, J. Comput. Appl. Math. 222 (2008), pp. 210–227. doi: 10.1016/j.cam.2007.10.035
   Web of Science ®Google Scholar
• A. La Rocca, A. Hernandez Rosales, and H. Power, Radial basis function Hermit collocation approach for the solution of time dependent convection diffusion problems, Eng. Anal. Boundary Elem. 29 (2005), pp. 359–370. doi: 10.1016/j.enganabound.2004.06.005
   Web of Science ®Google Scholar
• E. Larsson, K. Ahlander, and A. Hall, Multi-dimensional option pricing radial basis functions and the generalized Fourier transform, J. Comput. Appl. Math. 222 (2008), pp. 175–192. doi: 10.1016/j.cam.2007.10.039
   Web of Science ®Google Scholar
• C.K. Lee, X. Liu, and S. C. Fan, Local multiquadratic approximation for solving boundary value problems, Comput. Mech. 30 (2003), pp. 396–409. doi: 10.1007/s00466-003-0416-5
   Web of Science ®Google Scholar
• X. Liu and K. Tai, Point interpolation collocation method for the solution of partial differential equations, Eng. Anal. Boundary Elem. 30 (2006), pp. 598–609. doi: 10.1016/j.enganabound.2005.12.003
   Web of Science ®Google Scholar
• M.D. Marcozzi, S. Choi, and C.S. Chen, On the use of boundary condition for variational formulation arising in financial mathematics, Appl. Math. Comput. 124 (2001), pp. 197–214. doi: 10.1016/S0096-3003(00)00087-4
   Web of Science ®Google Scholar
• B.F. Nielsen, O. Skavhaug, and A. Tveito, Penalty and font-fixing methods for the numerical solution of American option probles, J. Comput. Financ. 5 (2002), pp. 69–97.
   Google Scholar
• B.F. Nielsen, O. Skavhaug, and A. Tveito, Penalty method for the numerical solution of American multi-asset option probles, J. Comput. Appl. Math. 222 (2008), pp. 3–16. doi: 10.1016/j.cam.2007.10.041
   Web of Science ®Google Scholar
• U. Pettersson, E. Larsson, G. Marcusson, and J. Persson, Improved radial basis function methods for multi-dimensional option pricing, J. Comput. Appl. Math. 222 (2008), pp. 82–93. doi: 10.1016/j.cam.2007.10.038
   Web of Science ®Google Scholar
• V.S.S.Y. Sanyasiraju and G. Chandhini, Local radial basis function based gridfree scheme for unsteady incompressible viscous flows, J. Comput. Phys. 227 (20) (2008), pp. 8922–8948. doi: 10.1016/j.jcp.2008.07.004
   Web of Science ®Google Scholar
• C. Shu, H. Ding, and K.S. Yeo, Local radial basis function based differential quadrature methods and its application to solve two dimensional incompressible Navier–Stokes equations, Comput. Methods Appl. Mech. Eng. 192 (2003), pp. 941–954. doi: 10.1016/S0045-7825(02)00618-7
   Web of Science ®Google Scholar
• G.B. Wright and B. Fornberg, Scattered node compact finite difference type formulas generated from radial basis functions, J. Comput. Phys. 212 (2006), pp. 99–123. doi: 10.1016/j.jcp.2005.05.030
   Web of Science ®Google Scholar
• M. Zerroukat, H. Power, and C.S. Chen, A numercical method for heat transfer problem using collocation and radial basis function, Int. J. Numer. Methods Eng. 42 (1998), pp. 1263–1278. doi: 10.1002/(SICI)1097-0207(19980815)42:7<1263::AID-NME431>3.0.CO;2-I
   Web of Science ®Google Scholar