A Review of the Binomial and Trinomial Models for Option Pricing and their Convergence to the Black-Scholes Model Determined Option Prices

Akerlof, G. (2002). Behavioral macroeconomics and macroeconomic behavior. The American Economic Review, 92(3), 411-433.10.1257/00028280260136192Search in Google Scholar

Bates, D. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutschemark options. Review of Financial Studies, (9), 69-108.10.1093/rfs/9.1.69Search in Google Scholar

Black, F., and Scholes, M. (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3), 637-654.10.1086/260062Search in Google Scholar

Bowei, C., and Wang, J. (2015). A lattice framework for pricing display and options with the stochastic volatility model. Electronic Commerce Research and Applications, 14(6), 465-479.10.1016/j.elerap.2015.07.002Search in Google Scholar

Boyle, P. (1986). Option valuation using a three-jump process. International Options Journal, (3), 7-12.Search in Google Scholar

Boyle, P. (1988). A lattice framework for option pricing with two state variables. Journal of Financial and Quantitative Analysis, 3, 1-12.10.2307/2331019Search in Google Scholar

Campbell, J., and Shiller, R. J. (1987). Cointegration and tests of present value models. Journal of Political Economy, (97), 1062-1088.10.1086/261502Search in Google Scholar

Carr, P., and Madan, B. D. (1999). Option valuation using the fast Fourier transform. Quantitative Finance, (1), 19-37.10.21314/JCF.1999.043Search in Google Scholar

Cootner, P. H. (1964). The random character of stock market prices. Cambridge, Mass.: MIT Press.Search in Google Scholar

Cox, J. C., and Ross, S. A. (1975). The pricing of options for Jump processes. Rodney L. White Center for Financial Research (Working Paper No. 2-75). University of Pennsylvania, Philadelphia, PA.Search in Google Scholar

Cox, J. C., and Ross, S. A. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics, (3), 145-166.10.1016/0304-405X(76)90023-4Search in Google Scholar

Cox, J. C., Ross, S. A., and Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229.10.1016/0304-405X(79)90015-1Search in Google Scholar

Fama, E. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25(2), 383-417.10.2307/2325486Search in Google Scholar

Gurdip, B., and Chen, Z. (1997). An alternative valuation model for contingent claims. Journal of Financial Economics, 44(1), 123-165.10.1016/S0304-405X(96)00009-8Search in Google Scholar

Haahtela, T. (2010). Recombining trinomial tree for real option valuation with changing volatility. Aalto University (Working Paper Series).10.2139/ssrn.1932411Search in Google Scholar

Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, (6), 327-343.10.1093/rfs/6.2.327Search in Google Scholar

Hull, J. C. (2017). Options, Futures, and Other Derivatives, Pearson.Search in Google Scholar

Jarrow, R., and Rudd, A. (1983). Option pricing. Homewood, Illinois.Search in Google Scholar

Kamrad, B., and Ritchken, P. (1991). Multinomial approximating models for option with k states variables. Management Sciences, 37(23), 1640-1652.10.1287/mnsc.37.12.1640Search in Google Scholar

Kiyosi, I. (1944). Stochastic integral. Proc. Imperial Acad. Tokyo, (20), 519-524.Search in Google Scholar

Leisen, D., and Reimer, M. (1996). Binomial models for option valuation – examining and improving convergence. Applied Mathematical Finance, 3(4), 319-346.10.1080/13504869600000015Search in Google Scholar

Merton, R. C. (1973), Theory of rational option pricing. Bell Journal of Economics, 4(1), p. 141-183.10.2307/3003143Search in Google Scholar

Merton, R. C. (1973a). Continuous-time speculative processes’: Appendix to Paul A. Samuelson’s ‘mathematics of speculative price’. SIAM Review 15 (January 1973), 34-38.Search in Google Scholar

Merton, R. C. (1973b). An intertemporal capital asset pricing model. Econometrica, 41(5), 867-887.10.2307/1913811Search in Google Scholar

Merton, R. C. (1973c). The relationship between put and call option prices: Comment. Journal of Finance, 28(1), 183-184.10.1111/j.1540-6261.1973.tb01357.xSearch in Google Scholar

Merton, R. C. (1975). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, (3), 125-144.Search in Google Scholar

Merton, R. C., and Samuleson, P. (1974). Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods. Journal of Financial Economics, 1(1), 67-94.10.1016/0304-405X(74)90009-9Search in Google Scholar

Peizer, D. B., and Pratt, J. W. (1968). A normal approximation for binomial, f, beta, and other common related tail probabilities, I, The Journal of the American Statistical Association, (63), 1416-1456.10.1080/01621459.1968.10480938Search in Google Scholar

Pratt, J. W. (1968). A normal approximation for binomial, f, beta, and other common, related tail probabilities, II. The Journal of the American Statistical Association, (63), 1457-1483.Search in Google Scholar

Puspita, E., Agustina, F., and Sispiyati, R. (2013). Convergence numerically of trinomial model in European option pricing. International Research Journal of Business Studies, 6(3), 195-201.10.21632/irjbs.6.3.195-201Search in Google Scholar

Rendleman, R., and Bartter, B. (1979). Two-state option pricing. Journal of Finance, (24), 1093-1110.10.1111/j.1540-6261.1979.tb00058.xSearch in Google Scholar

Rendleman, R., and Bartter, B. (1980). The pricing of options on debt securities. Journal of Financial and Quantitative Analysis, (15), 11-24.10.2307/2979016Search in Google Scholar

Romer, D. H. (1993). Rational asset-price movements without news. The American Economic Review, 83(5), 1112-1130.Search in Google Scholar

Ross, S., (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13(3), 341-360. doi:10.1016/0022-0531(76)90046-610.1016/0022-0531(76)90046-6Search in Google Scholar

Samuelson, P. A. (1965). Rational theory of warrant pricing. Industrial Management Review, (6), 13-31.Search in Google Scholar

Scott, L. (1997). Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Application of Fourier inversion methods. Mathematical Finance, (7), 413-426.10.1111/1467-9965.00039Search in Google Scholar

Smith, C. W. (1976). Option pricing: A review. Journal of Financial Economics, 3(1-2), 3-51.10.1016/0304-405X(76)90019-2Search in Google Scholar

Tian, Y. (1993). A modified lattice approach to option pricing. Journal of Futures Markets, 13(5), 563-577.10.1002/fut.3990130509Search in Google Scholar

Trigeorgis, L. (1991). A log-transformed binomial analysis method for valuing complex multi-option investments. Journal of Financial and Quantitative Analysis, 26(3), 309-326.10.2307/2331209Search in Google Scholar

Wilmott, P., Howison, S., and Dewynne, J. (1997). The mathematics of financial derivatives: A student introduction (2 ed.). Cambridge University Press.Search in Google Scholar