Abstract
In this chapter, we show how to use binomial and mutinomial distributions to derive option pricing models. In addition, we show how the Black and Scholes option pricing model is a limited case of binomial and multinomial option pricing model. Finally, a lattice framework of option pricing model is discussed in some detail.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Assume that the price movement of JNJ stock today is completely independent of its movement in the past.
Bibliography
Bhattacharya, R. N., & Rao, R. R. (1976). Normal approximation and asymptotic expansions. New York: Wiley.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 3, 637–659.
Boyle, P. (1988). A lattice framework for option pricing with two state variables. Journal of Financial and Quantitative Analysis, 23, 1–12.
Boyle, P. P. (1989). The quality option and the timing option in futures contracts. Journal of Finance, 44, 101–103.
Cox, J. C., & Rubinstein, M. (1985). Option markets. Englewood Cliffs, NJ: Prentice-Hall.
Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simple approach. Journal of Financial Economics, 7, 229–263.
Hull, J. (2014). Options, futures, and other derivatives (9th ed.). Prentice Hall.
Jarrow, R., & Turnbull, S. (1999). Derivatives securities (2nd ed.). South-Western College Publishing.
Johnson, H. (1981). The pricing of complex options. Unpublished manuscript.
Johnson, H. (1987). Options on the maximum or the minimum of several assets. Journal of Financial and Quantitative Analysis, 22, 277–283.
Lee, J. C. (2001). Using microsoft excel and decision trees to demonstrate the binomial option pricing model. Advances in Investment Analysis and Portfolio Management, 8, 303–329.
Lee, C. F., & Chen, Y. (2016). Alternative methods to derive option pricing models: Review and comparison. Review of Quantitative Finance and Accounting, 47(2), 417–451.
Lee, C. F., & Lee, J. C. (2010a). Multinomial option pricing model. Handbook of quantitative finance and risk management (pp. 399–406). New York: Springer.
Lee, C. F., & Lee, J. C. (2010b). Applications of the binomial distribution to evaluate call options. Handbook of quantitative finance and risk management (pp. 393–397). New York: Springer.
Lee, C. F., & Lee, A. C. (2013). Encyclopedia of finance (2nd ed.). New York, NY: Springer.
Lee, J. C., Lee, C. F., Wang, R. S., & Lin, T. I. (2004). On the limit properties of binomial and multinomial option pricing models: Review and integration. In Advances in quantitative analysis of finance and accounting new series volume 1 (Vol. 1). Singapore: World Scientific.
Lee, C. F., Lee, A. C., & Lee, J. (2010). Handbook of quantitative finance and risk management. New York: Springer.
Lee, C. F., Lee, J. C., & Lee, A. C. (2013). Statistics for business and financial economics. Singapore: World Scientific Publishing Company.
MacBeth, J., & Merville, L. (1979). An empirical examination of the Black–Scholes call option pricing model. The Journal of Finance, 34, 1173–1186.
Madan, D. B., Milne, F., & Shefrin, H. (1989). The multinomial option pricing model and its Brownian and Poisson limits. The Review of Financial Studies, 2(2), 251–265.
Rendelman, R. J., Jr., & Bartter, B. J. (1979). Two-state option pricing. Journal of Finance, 34(5), 1093–1110.
Stulz, R. (1982). Options on the minimum or the maximum of two risky assets: analysis and applications. Journal of Financial Economics, 10(2), 161–185.
Stulz, R., & Johnson, H. (1985). An analysis of secured debt. Journal of Financial Economics, 14(4), 501–521.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Science+Business Media, LLC, part of Springer Nature
About this chapter
Cite this chapter
Lee, CF., Chen, HY., Lee, J. (2019). The Binomial, Multinomial Distributions, and Option Pricing Model. In: Financial Econometrics, Mathematics and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9429-8_12
Download citation
DOI: https://doi.org/10.1007/978-1-4939-9429-8_12
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-9427-4
Online ISBN: 978-1-4939-9429-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)