A robust upwind difference scheme for pricing perpetual American put options under stochastic volatility

References

• Bakshi , G. , Cao , C. and Chen , Z. 1997 . Empirical performance of alternative option pricing models . J. Finance , 52 ( 5 ) : 2003 – 2049 .
   Web of Science ®Google Scholar
• Ball , C. A. and Roma , A. 1994 . Stochastic volatility option pricing . J. Finan. Quant. Anal. , 29 : 589 – 607 .
   Web of Science ®Google Scholar
• Black , F. and Scholes , M. 1973 . The pricing of options and corporate liabilities . J. Polit. Economy , 81 : 637 – 654 .
   Web of Science ®Google Scholar
• Brandt , A. and Cryer , C. W. 1983 . Multigrid algorithms for the solution of linear complementarity problems arising from free boundary problems . SIAM J. Sci. Stat. Comput. , 4 : 655 – 684 .
   Web of Science ®Google Scholar
• Cheng , X. and Xue , L. 2006 . On the error estimate of finite difference method for the obstacle problem . Appl. Math. Comput. , 183 : 416 – 422 .
   Web of Science ®Google Scholar
• Clarke , N. and Parrott , K. 1999 . Multigrid for American option pricing with stochastic volatility . Appl. Math. Finance , 6 ( 3 ) : 177 – 195 .
   Google Scholar
• Cryer , C. W. 1971 . The solution of a quadratic programming problem using systematic overrelaxation . SIAM J. Control Optim. , 9 ( 3 ) : 385 – 392 .
   Web of Science ®Google Scholar
• Fouque , J.-P. , Papanicolaou , G. and Sircar , K. R. 2000 . Derivatives in Financial Markets with Stochastic Volatilities , Cambridge : Cambridge University Press .
   Google Scholar
• Goeleven , D. 1996 . A uniqueness theorem for the generalized-order linear complementary problem associated with M-matrices . Linear Algebra Appl. , 235 : 221 – 227 .
   Web of Science ®Google Scholar
• Heston , S. 1993 . A closed-form solution for options with stochastic volatility with applications to bond and currency options . Rev. Finan. Stud. , 6 : 327 – 343 .
   Web of Science ®Google Scholar
• Huang , J. and Pang , J.-S. 1998 . Option pricing and linear complementarity . J. Comput. Finance , 2 : 31 – 60 .
   Google Scholar
• Hull , J. and White , A. 1987 . The pricing of options on assets with stochastic volatilities . J. Finance , 42 : 281 – 300 .
   Web of Science ®Google Scholar
• Ikonen , S. and Toivanen , J. 2007 . Componentwise splitting methods for pricing American options under stochastic volatility . Int. J. Theor. Appl. Finance , 10 : 331 – 361 .
   Google Scholar
• Ikonen , S. and Toivanen , J. 2008 . Efficient numerical methods for pricing American options under stochastic volatility . Numer. Methods Partial Differ. Equ. , 241 ( 1 ) : 104 – 126 .
   Web of Science ®Google Scholar
• Ikonen , S. and Toivanen , J. 2009 . Operator splitting methods for American options under stochastic volatility . Numer. Math. , 113 : 299 – 324 .
   Web of Science ®Google Scholar
• Ito , K. and Toivanen , J. 2009 . Lagrange multiplier approach with optimized finite difference stencils for pricing American options under stochastic volatility . SIAM J. Sci. Comput. , 31 ( 4 ) : 2646 – 2664 .
   Web of Science ®Google Scholar
• Kangro , R. and Nicolaides , R. 2001 . Far field boundary conditions for Black–Scholes equations . SIAM J. Numer. Anal. , 38 : 1357 – 1368 .
   Web of Science ®Google Scholar
• Kellogg , R. B. and Tsan , A. 1978 . Analysis of some difference approximations for a singular perturbation problem without turning points . Math. Comp , 32 : 1025 – 1039 .
   Web of Science ®Google Scholar
• Oosterlee , C. W. 2003 . On multigrid for linear complementarity problems with applications to American-style options . Electron. Trans. Numer. Anal , 15 : 165 – 185 .
   Web of Science ®Google Scholar
• Tao , L. N. 1983 . The analytical and general solution of the Cauchy Stefan problem . Quart. J. Mech. Appl. Math. , 36 ( 4 ) : 487 – 504 .
   Web of Science ®Google Scholar
• Tompkins , R. G. 2001 . Stock index futures markets: Stochastic volatility and smiles . J. Futures Markets , 21 : 43 – 78 .
   Web of Science ®Google Scholar
• Wilmott , P. , Dewynne , J. and Howison , S. 1993 . Option Pricing: Mathematical Models and Computation , Oxford : Oxford Financial Press .
   Google Scholar
• Zhu , S.-P. and Chen , W.-T. 2011 . A predictor–corrector scheme based on the ADI method for pricing American puts with stochastic volatility . Comput. Math. Appl. , 62 ( 1 ) : 1 – 26 .
   Web of Science ®Google Scholar
• Zhu , S.-P. and Chen , W.-T. 2011 . A spectral-collocation method for pricing perpetual American puts with stochastic volatility . Appl. Math. Comput. , 217 ( 22 ) : 9033 – 9040 .
   Web of Science ®Google Scholar
• Zvan , R. , Forsyth , P. A. and Vetzal , K. R. 1998 . Penalty methods for American options with stochastic volatility . J. Comput. Appl. Math. , 91 ( 2 ) : 199 – 218 .
   Web of Science ®Google Scholar