References
- Abramowitz , M. and Stegun , I. A. 1965 . “ Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables ” . New York , NY : Dover Publications .
- Alexander , C. 2008 . “ Market Risk Analysis IV: Value at Risk Models ” . Chichester : John Wiley & Sons, Ltd .
- Avellaneda , M. , Levy , A. and Para , A. 1995 . Pricing and hedging derivative securities in markets with uncertain volatilities . Appl. Math. Finance , 2 : 73 – 88 .
- Brennan , M. J. and Schwartz , E. S. 1977 . The valuation of American put options . J. Finance , 32 ( 2 ) : 449 – 462 .
- Fama , E. 1965 . The behavior of stock market prices . J. Bus. , 38 : 34 – 105 .
- Gautschi , W. 1982 . On generating orthogonal polynomials . SIAM J. Sci. Stat. Comput. , 3 ( 3 ) : 289 – 317 .
- Ghanem , R. G. and Spanos , P. D. 1991 . “ Stochastic Finite Elements: A Spectral Approach ” . New York , NY : Springer-Verlag .
- Glasserman , P. 2004 . “ Monte Carlo Methods in Financial Engineering ” . New York : Springer-Verlag Inc. .
- Heston , S. L. 1993 . A closed-form solution for option with stochastic volatility with applications to bond and currency options . Rev. Financ. Stud. , 6 : 327 – 343 .
- Ikonen , S. and Toivanen , J. 2007 . Pricing American options using LU decomposition . Appl. Math. Sci. , 1 : 2529 – 2551 .
- Kopriva , D. A. 2009 . “ Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers ” . Dordrecht, Heidelberg, London, New York : Springer .
- Longstaff , F. A. and Schwartz , E. S. 2001 . Valuing American options by simulation: A simple least-squares approach . Rev. Financ. Stud. , 14 : 113 – 147 .
- Lyons , T. J. 1995 . Uncertain volatility and the risk-free synthesis of derivatives . Appl. Math. Finance , 2 : 117 – 133 .
- Maître , O. L. and Knio , O. 2010 . “ Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics ” . Dordrecht, Heidelberg, London, New York : Springer .
- Myneni , R. 1992 . The pricing of the American option . Ann. Appl. Probab. , 2 : 1 – 23 .
- Pulch , R. and van Emmerich , C. 2009 . Polynomial chaos for simulating random volatilities . Math. Comput. Simulation , 80 : 245 – 255 .
- Shreve , S. E. 2004 . “ Stochastic Calculus for Finance II: Continuous Time Models ” . New York : Springer .
- Silverman , B. 1998 . “ Density Estimation for Statistics and Data Analysis ” . New York : Chapman & Hall/CRC .
- Walters , R. and Huyse , L. 2002 . “ Uncertainty analysis for fluid mechanics with applications ” . Hampton , VA ICASE. Rep. 2002-1
- Wan , X. and Karniadakis , G. M. 2006 . Long-term behavior of polynomial chaos in stochastic flow simulations . Comput. Methods Appl. Mech. Engrg. , 195 : 5582 – 5596 .
- Wilmott , P. and Oztukel , A. 1998 . Uncertain parameters, an emperical stochastic volatilty model and confidence limits . Int. J. Theor. Appl. Finance , 1 : 175 – 189 .
- Willmot , P. , Dewyne , J. and Howison , S. 1993 . “ Option Pricing: Mathematical Models and Computation ” . Oxford, England : Oxford Financial Press .
- Xiu , D. 2009 . Fast numerical methods for stochastic computations: A review . Comm. Comput. Phys. , 5 : 242 – 272 .
- Xiu , D. 2010 . “ Numerical Methods for Stochastic Computations: A Spectral Method Approach ” . Princeton , NJ : Princeton University Press .
- Xiu , D. and Karniadakis , G. 2002 . The Wiener–Askey polynomial chaos for stochastic differential equations . SIAM J. Sci. Comput. , 24 : 619 – 644 .
- Zhu , S. P. 2006 . An exact and explicit solution for the valuation of American put options . Quant. Finance , 6 : 229 – 242 .