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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 246724, 11 pages
Removing the Correlation Term in Option Pricing Heston Model: Numerical Analysis and Computing
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Received 23 March 2013; Revised 18 May 2013; Accepted 20 May 2013
Academic Editor: T. Diagana
Copyright © 2013 R. Company et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- B. Dupire, “Arbitrage pricing with stochastic volatility,” Tech. Rep., Banque Paribas Swaps and Options Research Team Monograph, 1993.
- J. Hull and A. White, “The pricing of options with stochastic volatilities,” Journal of Finance, vol. 42, pp. 281–300, 1987.
- S. L. Heston, “A closed-form solution for options with stochastic volatility with applications to bond and currency options,” The Review of Financial Studies, vol. 6, pp. 327–343, 1993.
- P. Hagan, D. Kumar, and A. S. Lesniewski, “Managing smile risk,” Wilmott Magazine, vol. 15, pp. 84–108, 2002.
- A. Pascucci, PDE and Martingale Methods in Option Pricing, vol. 2 of Bocconi & Springer Series, Springer, Milan, Italy, 2011.
- S. Mikhailov and U. Nögel, “Heston's stochastic volatility model implementation, calibration and some extensions,” Wilmott Magazine, vol. 4, pp. 74–79, 2003.
- A. Elices, “Models with time-dependent parameters using transform methods: application to Heston's model,” http://arxiv.org/abs/0708.2020.
- E. Benhamou, E. Gobet, and M. Miri, “Time dependent Heston model,” SIAM Journal on Financial Mathematics, vol. 1, pp. 289–325, 2010.
- N. Hilber, A. M. Matache, and C. Schwab, “Sparse wavelet methods for option pricing under stochastic volatility,” Journal of Computational Finance, vol. 8, no. 4, pp. 1–42, 2005.
- W. Zhu and D. A. Kopriva, “A spectral element approximation to price European options with one asset and stochastic volatility,” Journal of Scientific Computing, vol. 42, no. 3, pp. 426–446, 2010.
- N. Clarke and K. Parrott, “Multigrid for american option pricing with stochastic volatility,” Applied Mathematical Finance, vol. 6, no. 3, pp. 177–195, 1999.
- R. Sheppard, Pricing equity derivatives under stochastic volatility: a partial differential equation approach [Ph.D. thesis], Faculty of Science, University of the Witwatersrand, 2007.
- B. Düring and M. Fournié, “High-order compact finite difference scheme for option pricing in stochastic volatility models,” Journal of Computational and Applied Mathematics, vol. 236, no. 17, pp. 4462–4473, 2012.
- D. J. Duffy, Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach, vol. 312, John Wiley & Sons, Chichester, UK, 2006.
- K. J. Hout and S. Foulon, “ADI finite difference schemes for option pricing in the Heston model with correlation,” International Journal of Numerical Analysis and Modeling, vol. 7, no. 2, pp. 303–320, 2010.
- R. Zvan, P. A. Forsyth, and K. R. Vetzal, “Negative coefficients in two-factor 25 option pricing models,” Journal of Computational Finance, vol. 7, no. 1, pp. 37–73, 2003.
- G. H. Golub and C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, London, UK, 3rd edition, 1996.
- R. Company, L. Jódar, and J.-R. Pintos, “Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs,” Mathematical Modelling and Numerical Analysis, vol. 43, no. 6, pp. 1045–1061, 2009.
- R. Company, L. Jódar, and J.-R. Pintos, “Numerical analysis and computing for option pricing models in illiquid markets,” Mathematical and Computer Modelling, vol. 52, no. 7-8, pp. 1066–1073, 2010.
- M.-C. Casabán, R. Company, L. Jódar, and J.-R. Pintos, “Numerical analysis and computing of a non-arbitrage liquidity model with observable parameters for derivatives,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 1951–1956, 2011.
- P. R. Garabedian, Partial Differential Equations, AMS Chelsea, Providence, RI, USA, 1998.
- R. Ehrhardt, Discrete artificial boundary conditions [Ph.D. thesis], Technische Universitat Berlin, 2001.
- R. Kangro and R. Nicolaides, “Far field boundary conditions for Black-Scholes equations,” SIAM Journal on Numerical Analysis, vol. 38, no. 4, pp. 1357–1368, 2000.
- M. Ehrhardt and R. E. Mickens, “A fast, stable and accurate numerical method for the Black-Scholes equation of American options,” International Journal of Theoretical and Applied Finance, vol. 11, no. 5, pp. 471–501, 2008.
- G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Clarendon Press, Oxford, UK, 3rd edition, 1985.