Exponentially fitted block backward differentiation formulas for pricing options

References

• Akinfenwa, O. A., Jator, S. N., & Yao, N. M. (2013). Continuous block backward differentiation formula for solving stiff ordinary differential equations. Computers & Mathematics with Applications, 65(7), 996–18. https://doi.org/10.1016/j.camwa.2012.03.111
   Web of Science ®Google Scholar
• Cash, J. R. (1980). On integration on stiff system of ordinary differential equations using extended bdf. Numer Math, 34(3), 235–246. https://doi.org/10.1007/BF01396701
   Web of Science ®Google Scholar
• Cash, J. R. (1984). Two new finite diference schemes for parabolic equations. SIAM Journal of Numerical Analysis, 21(3), 433–446. https://doi.org/10.1137/0721032
   Web of Science ®Google Scholar
• Chawla, M. M., Al-Zanaidia, M. A., & Evans, D. J. (2003). Generalized trapezoidal formulas for the Black-Scholes equation of option pricing. International Journal of Computer Mathematics, 80(12), 1521–1526. https://doi.org/10.1080/00207160310001603299
   Web of Science ®Google Scholar
• Coleman, J., & Duxbury, S. C. (2000). Mixed collocation methods for y=f(x,y). Journal of Computational and Applied Finance, 26(1–2), 47–75. https://doi.org/10.1016/S0377-0427(99)00340-4
   Web of Science ®Google Scholar
• Gear, C. (1971). Numerical initial value problems in ordinary differential equations. Prentice-Hall.
   Google Scholar
• Geske, R., & Johnson, H. E. (1984). The American put option valued analytically. Journal of Finance, 39(5), 1511–1524. https://doi.org/10.1111/j.1540-6261.1984.tb04921.x
   Web of Science ®Google Scholar
• Giles, M., & Carter, R. (2006). Convergence analysis of Crank-Nicolson and Rannacher time-marching. Journal of Computational Finance, 9(4), 89–112. https://doi.org/10.21314/JCF.2006.152
   Google Scholar
• Huang, H.-Z., Subrahmanyam, M., & Yu, G. (1996). Pricing and hedging American options: A recursive integration method. Rev. Finan. Stud., 9(1), 277–300. https://doi.org/10.1093/rfs/9.1.277
   Web of Science ®Google Scholar
• Hull, J. (2015). Options, futures, and other derivatives (9th ed.). Pearson.
   Google Scholar
• Jator, S. N., & Nyonna, D. Y. (2014). Extended block backward differentiation formula for the valuation of options. Communications in Mathematical Finance, 3(2), 1-19. ISSN: 2241-1968. http://www.scienpress.com/Upload/CMF/Vol%203_2_1.pdf
   Google Scholar
• Khaliq, A. Q. M., Voss, D. A., & Kazmi, S. H. K. (2006). A linear implicit predictor-corrector scheme for pricing American options using a penalty method approach. Journal of Banking and Finance, 30(2), 489–502. https://doi.org/10.1016/j.jbankfin.2005.04.017
   Web of Science ®Google Scholar
• Lambert, J. D. (1991). Numerical methods for ordinary differential systems. John Wiley.
   Google Scholar
• Le Floch, F. (2014). Tr-bdf2 for fast stable American option pricing. Risk, 17, 31-56. https://www.risk.net/journal-of-computational-finance/2330321/tr-bdf2-for-fast-stable-american-option-pricing
   Google Scholar
• Liao, W., & Khaliq, A. Q. M. (2009). High-order compact scheme for solving nonlinear Black-Scholes equation with transaction cost. International Journal of Computer Mathematics, 86(6), 1009–1023. https://doi.org/10.1080/00207160802609829
   Web of Science ®Google Scholar
• Merton, R. (1973). The theory of rational option pricing. The Bell Journal of Economics and Management Science, 4(1), 141. https://doi.org/10.2307/3003143
   Google Scholar
• Ndukum, P. L., Biala, T. A., Jator, S. N., & Adeniyi, R. B. (2016). On a family of trigonometrically fitted extended backward differentiation formulas for stiff and oscillatory initial value problems. Numerical Algorithms, 74(1), 267–287. https://doi.org/10.1007/s11075-016-0148-1
   Web of Science ®Google Scholar
• Nguyen, H., Sidje, R., & Nguyen, H. (2007). Analysis of trigonometric implicit Runge-Kutta methods. Journal of Computational and Applied Mathematics, 198(1), 187–207. https://doi.org/10.1016/j.cam.2005.12.006
   Web of Science ®Google Scholar
• Oosterlee, C., Leentvaar, X., C., C. W., & Huang. (2005). Accurate American option pricing by grid stretching and high-order finite differences. Working Papers, DIAM, Delft University of Technology, the Netherlands.
   Google Scholar
• Ramos, H., & Vigo-Aguiar, J. (2007). A fourth-order Runge-Kutta method based on BdF-type Chebyschev approximations. Journal of Computational and Applied Mathematics, 204(1), 124–136. https://doi.org/10.1016/j.cam.2006.04.033
   Web of Science ®Google Scholar
• Tangman, D., Gopaul, A., & Bhuruth, M. (2008). Exponential time integration and Cheby-chev discretization schemes for fast pricing of options. Applied Numerical Mathemaics, 58(9), 1309–1319. https://doi.org/10.1016/j.apnum.2007.07.005
   Web of Science ®Google Scholar
• Wilmott, P., Howison, S., & Dewynne, J. (2009). The mathematics of financial derivatives: A student introduction. Cambridge Univ. Press.
   Google Scholar