Multinomial method for option pricing under Variance Gamma

References

• Y. Ait-Sahalia and J. Jacod, Analyzing the spectrum of asset returns: Jump and volatility components in high frequency data, J. Econ. Lit. 50(4) (2012), pp. 1007–1050. doi: 10.1257/jel.50.4.1007
   Web of Science ®Google Scholar
• A. Almendral, Numerical valuation of American options under the CGMY process, in Exotic Option Pricing and Advanced Levy Models, A.E. Kyprianou, W. Schoutens, and P. Wilmott, eds., Wiley, Hoboken, 2005.
   Google Scholar
• A. Almendral and C.W. Oosterlee, On American options under the Variance Gamma process, Appl. Math. Finan. 14(2) (2007), pp. 131–152. doi: 10.1080/13504860600724885
   Google Scholar
• D. Applebaum, Lévy Processes and Stochastic Calculus, 2nd ed., Cambridge University Press, Cambridge, 2009.
   Google Scholar
• O.E. Barndorff-Nielsen, Processes of Normal inverse Gaussian type, Finance and Stochastics Financ. Stoch. 2 (1997), pp. 41–68. doi: 10.1007/s007800050032
   Google Scholar
• F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81(3) (1973), pp. 637–654. doi: 10.1086/260062
   Web of Science ®Google Scholar
• P. Carr and D. Madan, Option valuation using the Fast Fourier transform, J. Comput. Financ. 2 (1999), pp. 61–73. doi: 10.21314/JCF.1999.043
   Google Scholar
• R. Cont and P. Tankov, Financial Modelling with Jump Processes, 1 ed., Chapman and Hall/CRC, London, 2003.
   Google Scholar
• R. Cont and E. Voltchkova, A finite difference scheme for option pricing in jump diffusion and exponential Lévy models, SIAM J. Numer. Anal. 43(4) (2005), pp. 1596–1626. doi: 10.1137/S0036142903436186
   Web of Science ®Google Scholar
• J. Cox, S. Ross, and M. Rubinstein, Option pricing: A simplified approach, J. Financ. Econ. 7 (1979), pp. 229–263. doi: 10.1016/0304-405X(79)90015-1
   Web of Science ®Google Scholar
• E. Eberlein and U. Keller, Hyperbolic distributions in finance, Bernoulli 1(3) (1995), pp. 281–299. doi: 10.2307/3318481
   Google Scholar
• M.C. Fu, Variance-Gamma and Monte Carlo, Adv. Math. Financ. (2000), pp. 21–34.
   Google Scholar
• H. Geman, D. Madan, and M. Yor, Asset prices are Brownian motion: Only in business time, in Quantitative Analysis in Financial Markets: Collected Papers of the New York University Mathematical Finance Seminar, Vol. 2(1), 1998, pp. 103–146.
   Google Scholar
• D. Hainaut and R. MacGilchrist, An interest tree driven by a Lévy process, J. Derivat. 18(2) (2010), pp. 33–45. doi: 10.3905/jod.2010.18.2.033
   Web of Science ®Google Scholar
• A. Hirsa and D. Madan, Pricing American options under Variance Gamma, J. Comput. Financ. 7 (2001), pp. 63–80. doi: 10.21314/JCF.2003.112
   Google Scholar
• E. Kellezi and N. Webber, Valuing Bermudan options when asset returns are Lévy processes, Quant. Financ. 4(1) (2004), pp. 87–100. doi: 10.1088/1469-7688/4/1/008
   Web of Science ®Google Scholar
• F.A. Longstaff and E.S. Schwartz, Valuing American options by simulation: A simple Least-Squares approach, Rev. Financial Stud. 14 (2001), pp. 113–147. doi: 10.1093/rfs/14.1.113
   Web of Science ®Google Scholar
• D. Madan, P. Carr, and E. Chang, The variance Gamma process and option pricing, Europ. Finance Rev. 2 (1998), pp. 79–105. doi: 10.1023/A:1009703431535
   Google Scholar
• D.B. Madan and F. Milne, Option pricing with V.G. martingale components, Math. Finan. 1 (1991), pp. 39–55. doi: 10.1111/j.1467-9965.1991.tb00018.x
   Google Scholar
• D. Madan and E. Seneta, The Variance Gamma (V.G.) model for share market returns, J. Bus. 63(4) (1990), pp. 511–524. doi: 10.1086/296519
   Web of Science ®Google Scholar
• R.A. Maller, D.H. Solomon, and A. Szimayer, A multinomial approximation for American option prices in Lévy process models, Math. Finan. 16(4) (2006), pp. 613–633. doi: 10.1111/j.1467-9965.2006.00286.x
   Web of Science ®Google Scholar
• K.I. Sato, Lévy processes and infinitely divisible distributions, Cambridge University Press, Cambridge, 1999.
   Google Scholar
• E. Seneta, Fitting the Variance-Gamma model to financial data, J. Appl. Probab. 41 (2004), pp. 177–187. doi: 10.1017/S0021900200112288
   Web of Science ®Google Scholar
• C.S. Ssebugenyi, I.J. Mwaniki, and V.S. Konlack, On the minimal entropy martingale measure and multinomial lattices with cumulants, Appl. Math. Finan. 20(4) (2013), pp. 359–379. doi: 10.1080/1350486X.2012.714226
   Google Scholar
• Y. Yamada and J. Primbs, Construction of Multinomial Lattice Random Walks for Optimal Hedges, in Proceeding of the 2001 International Conference of Computational Science, San Francisco, CA, USA, 2001, pp. 579–588.
   Google Scholar
• Y. Yamada and J. Primbs, Mean Square Optimal Hedges using Higher Order Moments, in Proceeding of the 2003 International Conference on Computational Intelligence for Financial Engineering, IEEE, Hong Kong, 2003.
   Google Scholar
• Y. Yamada and J.A. Primbs, Properties of multinomial lattices with cumulants for option pricing and hedging, Asia-Pacific Finan. Markets 11 (2004), pp. 335–365. doi: 10.1007/s10690-005-9005-2
   Google Scholar