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Research Papers

Valuation of American options under the CGMY model

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Pages 1529-1539 | Received 31 Mar 2015, Accepted 18 Feb 2016, Published online: 22 Apr 2016

References

  • Ahn, C.M. and Thompson, H.E., The impact of jump risks on nominal interest rates and foreign exchange rates. Rev. Quant. Finance Account., 1992, 2, 17–31.
  • Almendral, A. and Oosterlee, C.W., Accurate evaluation of European and American options under the CGMY process. SIAM J. Sci. Comput., 2007, 29, 93–117.
  • Ballotta, L. and Kyriakou, I., Monte Carlo simulation of the CGMY process and option pricing. J. Futures Markets, 2014, 34, 1095–1121.
  • Barndorff-Nielsen, O.E., Normal inverse Gaussian distributions and stochastic volatility modelling. Scand. J. Stat., 1997, 24, 1–13.
  • Barndorff-Nielsen, O.E., Exponentially decreasing distributions for the logarithm of particle size. Proc. R. Soc. London A, 1977, 353, 401–419.
  • Barndorff-Nielsen, O.E., Processes of normal inverse Gaussian type. Finance Stoch., 1998, 2, 41–68.
  • Barone-Adesi, G. and Whaley, R.E., Efficient analytic approximation of American option values. J. Finance, 1987, 42, 301–320.
  • Black, F. and Scholes, M., The pricing of options and corporate liabilities. J. Polit. Econ., 1973, 81, 637–654.
  • Boyarchenko S.I. and Levendorskiĭ S.Z., Non-Gaussian Merton--Black--Scholes Theory, 2002 (World Scientific: River Edge, NJ).
  • Brunner, H., Collocation Methods for Volterra Integral and Related Functional Differential Equations, 2004 (Cambridge University Press: Cambridge).
  • Burden, R.L. and Faires, J.D., Numerical Analysis, 2011 (Brooks/Cole: Boston, MA).
  • Carr, P., Geman, H., Madan, D.B. and Yor, M., The fine structure of asset returns: An empirical investigation. J. Bus., 2002, 75, 305–332.
  • Carr, P., Jarrow, R. and Myneni, R., Alternative characterizations of American put options. Math. Finance, 1992, 2, 87–106.
  • Carr, P. and Madan, D.B., Option valuation using the fast Fourier transform. J. Comput. Finance, 1999, 2, 61–73.
  • Carr, P. and Wu, L.R., The finite moment log-stable process and option pricing. J. Finance, 2003, 58, 753–778.
  • Cartea, Á. and Del-Castillo-Negrete, D., Fractional diffusion models of option prices in markets with jumps. Physica A, 2007, 374, 749–763.
  • Chiarella, C. and Ziogas, A., American call options under jump-diffusion processes–A Fourier transform approach. Appl. Math. Finance, 2009, 16, 37–79.
  • Cont, R. and Tankov, P., Financial Modelling with Jump Processes, 2004 (Chapman and Hall/CRC: Boca Raton, FL).
  • Derman, E. and Wilmott, P., The financial modelers’ manifesto. Derman’s Blog, 2009. Available online at: http://dx.doi.org/10.2139/ssrn.1324878.
  • Evans, J.D., Kuske, R. and Keller, J.B., American options on assets with dividends near expiry. Math. Finance, 2002, 12, 219–237.
  • Fang, F. and Oosterlee, C.W., Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions. Numer. Math., 2009, 114, 27–62.
  • Feng, L. and Lin, X., Pricing Bermudan options in Lévy process models. SIAM J. Financ. Math., 2013, 4, 474–493.
  • Halgree, C., Self-decomposability of the generalized inverse Gaussian and hyperbolic distributions. Z. Wahrscheinlichkeit., 1979, 47, 13–17.
  • Hirsa, A. and Madan, D.B., Pricing American options under variance gamma. J. Comput. Finance, 2004, 7, 63–80.
  • Jacka, S.D., Optimal stopping and the American put. Math. Finance, 1991, 1, 1–14.
  • Ju, N.J., Pricing an American option by approximating its early exercise boundary as a multi-piece exponential function. Rev. Financ. Stud., 1998, 11, 627–646.
  • Kellezi, E. and Webber, N., Valuing Bermudan options when assest returns are Lévy processes. Quant. Finance, 2004, 4, 87–100.
  • Kim, I.J., The analytic valuation of American options. Rev. Financ. Stud., 1990, 3, 547–572.
  • Koponen, I.T., Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process. Phys. Rev. E, 1995, 52, 1197–1199.
  • Kou, S., A jump-diffusion model for option pricing. Manage. Sci., 2002, 48, 1086–1101.
  • Kwok, Y.K., Mathematical Models of Financial Derivatives, 2008 (Springer-Verlag: Berlin, Heideberg).
  • Lee, R.W., Option pricing by transform methods: Extensions, unification, and error control. J. Comput. Finance, 2004, 7, 51–86.
  • Lewis, A.L., A simple option formula for general jump-diffusion and other exponential Lévy processes. Working Paper, 2001, Available online at SSRN: http://ssrn.com/abstract=282110.
  • Longstaff, F.A. and Schwartz, E.S., Valuing American options by simulation: A simple least-squares approach. Rev. Financ. Stud., 2001, 14, 113–147.
  • Lord, R., Fang, F., Bervoets, F. and Oosterlee, C.W., A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes. SIAM J. Sci. Comput., 2008, 30, 1678–1705.
  • MacMillan, L.W., Analytic approximation for the American put option. Adv. Futures Options Res., 1986, 1, 119–139.
  • Madan, D.B., Carr, P. and Chang, E., The variance gamma process and option pricing. Eur. Finance Rev., 1998, 2, 79–105.
  • Madan, D.B. and Seneta, E., Simulation of estimates using the empirical characteristic funtion. Int. Stat. Rev., 1987, 55, 153–161.
  • Madan, D.B. and Seneta, E., The variance gamma (VG) model for share market returns. J. Bus., 1990, 63, 511–524.
  • Madan, D.B. and Yor, M., Representing the CGMY and Meixner Lévy processes as time changed Brownian motions. J. Comput. Finance, 2008, 12, 27–47.
  • Maller, R.A., Solomon, D.H. and Szimayer, A., A multinomial approximation for American option prices in Lévy process models. Math. Finance, 2006, 16, 613–633.
  • Merton, R.C., Option pricing when underlying stock returns are discontinuous. J. Financ. Econ., 1976, 3, 125–144.
  • Rachev, S.T., Menn, C. and Fabozzi, F.J., Fat-tailed and Skewed Asset Return Distributions: Implications for Risk Management, Portfolio Selection, and Option Pricing, 2005 (John Wiley and Sons: Hoboken, NJ).
  • Raible, S., Lévy processes in finance: Theory, numerics and empirical facts. PhD thesis, Freiburg University, Germany, 1998.
  • Rydberg, T.H., The normal inverse Gaussian Lévy process: Simulation and approximation. Commun. Stat. Stoch. Models, 1997, 13, 887–910.
  • Shen, J., Tang, T. and Wang, L.-L., Spectral Methods: Algorithms, Analysis and Applications, 2011 (Springer: Berlin Heidelberg).
  • Wang, H., Wang, K. and Sircar, T., A direct O(N log\textsuperscript{2} N) finite difference method for fractional diffusion equations. J. Comput. Phys., 2010, 229, 8095–8104.

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