A stochastic approximation algorithm for option pricing model calibration with a switchable market

References

• Billingsley , P. 1968 . Convergence of Probability Measures , New York : John Wiley .
   Google Scholar
• Blanco , C. and Soronow , D. 2001 . Mean reverting processes – Energy price processes used for derivatives pricing and risk management . Commodities Now , : 68 – 72 .
   Google Scholar
• Bollen , N. P.B. 1998 . Valuing options in regime-switching models . J. Derivatives , 6 : 38 – 49 .
   Google Scholar
• Bos , L. P. , Ware , A. F. and Pavlov , B. S. 2002 . On a semi-spectral method for pricing an option on a mean-reverting asset . Quant. Financ. , 2 : 337 – 345 .
   Google Scholar
• Buffington , J. and Elliott , R. J. 2002 . American options with regime switching . Int. J. Theor. Appl. Financ. , 5 : 497 – 514 .
   Google Scholar
• Cowles , A. and Jones , H. 1937 . Some posteriori probabilities in stock market action . Econometrica , 5 : 280 – 294 .
   Web of Science ®Google Scholar
• de Jong , C. and Huisman , R. Option formulas for mean-reverting power prices with spikes . preprint
   Google Scholar
• Duan , J.-C. , Popova , I. and Ritchken , P. 2002 . Option pricing under regime switching . Quant. Financ. , 2 : 116 – 132 .
   Google Scholar
• Elliott , R. J. and Kopp , P. E. 1998 . Mathematics of Financial Markets , New York : Springer-Verlag .
   Google Scholar
• Ethier , S. N. and Kurtz , T. G. 1986 . Markov Process: Characterization and Convergence , New York : John Wiely .
   Google Scholar
• Fama , E. and French , K. R. 1988 . Permanent and temporary components of stock prices . J. Polit. Econ. , 96 : 246 – 273 .
   Web of Science ®Google Scholar
• Gallagher , L. A. and Taylor , M. P. 2002 . Permanent and temporary components of stock prices: Evidence from assessing macroeconomic shocks . South. Econ. J. , 69 : 345 – 362 .
   Web of Science ®Google Scholar
• Guo , X. 1999 . “ Inside information and stock fluctuations ” . Rutgers University . Ph.D. thesis
   Google Scholar
• Guo , X. 2001 . Inside information and option pricings . Quant. Financ. , 1 : 38 – 44 .
   Google Scholar
• Guo , X. 2001 . An explicit solution to an optimal stopping problem with regime switching . J. Appl. Probab. , 38 : 464 – 481 .
   Web of Science ®Google Scholar
• Guo , X. and Zhang , Q. 2005 . Optimal selling rules in a regime switching model . IEEE Trans. Autom. Control , 50 : 1450 – 1455 .
   Web of Science ®Google Scholar
• Hafner , C. M. and Herwartz , H. 2001 . Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis . J. Empir. Financ. , 8 : 1 – 34 .
   Google Scholar
• Hamilton , J. D. 1989 . A new approach to the economic analysis of non-stationary time series . Econometrica , 57 : 357 – 384 .
   Web of Science ®Google Scholar
• Hardy , M. R. 2001 . A regime-switching model of long-term stock returns . North Am. Actuar. J. , 5 : 41 – 53 .
   Google Scholar
• Hull , J. C. 1997 . Options, Futures, and Other Derivatives , 3 , Upper Saddle River, NJ : Prentice-Hall .
   Google Scholar
• Kushner , H. J. 1984 . Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory , Cambridge, MA : MIT Press .
   Google Scholar
• Kushner , H. J. and Yin , G. 2003 . Stochastic Approximation and Recursive Algorithms and Applications , 2 , New York : Springer .
   Google Scholar
• Song , Q. S. , Yin , G. and Zhang , Q. 2009 . Stochastic optimization methods for buying-low-and-selling-high strategies . Stoch. Anal. Appl. , 27 : 523 – 542 .
   Web of Science ®Google Scholar
• Yao , D. D. , Zhang , Q. and Zhou , X. Y. 2006 . A regime-switching model for European options, in Stochastic Processes, Optimization, and Control Theory Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems , Edited by: Yan , H. M. , Yin , G. and Zhang , Q. Vol. 94 , 281 – 300 . New York : Springer .
   Google Scholar
• Yin , G. 1991 . On extensions of Polyak's averaging approach to stochastic approximation . Stoc. Stoch. Rep. , 36 : 245 – 264 .
   Google Scholar
• Yin , G. and Zhang , Q. 2005 . Discrete-time Markov Chains: Two-time-scale Methods and Applications , New York : Springer .
   Google Scholar
• Yin , G. , Liu , R. H. and Zhang , Q. 2002 . Recursive algorithms for stock liquidation: A stochastic optimization approach . SIAM J. Optim. , 13 : 240 – 263 .
   Web of Science ®Google Scholar
• Yin , G. , Zhang , Q. and Zhuang , C. 2007 . Stochastic approximation algorithms for parameter estimation in option pricing with regime switching . Stoch. Anal. Appl. , 25 : 1243 – 1261 .
   Web of Science ®Google Scholar
• Yin , G. , Wang , J. W. , Zhang , Q. and Liu , Y. J. 2006 . Stochastic optimization algorithms for pricing American put options under regime-switching models . J. Optim. Theory Appl. , 131 : 37 – 52 .
   Web of Science ®Google Scholar
• Zhang , Q. 2001 . Stock trading: An optimal selling rule . SIAM J. Control Optim. , 40 : 64 – 87 .
   Web of Science ®Google Scholar
• Zhang , H. and Zhang , Q. 2008 . Trading a mean-reverting asset: Buy low and sell high . Automatica , 44 : 1511 – 1518 .
   Web of Science ®Google Scholar