Journal of Finance and Economics
ISSN (Print): 2328-7284 ISSN (Online): 2328-7276 Editor-in-chief: Suman Banerjee
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Journal of Finance and Economics. 2019, 7(3), 81-87
DOI: 10.12691/jfe-7-3-1
Open AccessArticle

### Pricing Options Using Trinomial Lattice Method

1School of Mathematics, University of Nairobi, Kenya

2Pan African University, Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya

Pub. Date: July 02, 2019

Cite this paper:
Kenneth Kiprotich Langat, Joseph Ivivi Mwaniki and George Korir Kiprop. Pricing Options Using Trinomial Lattice Method. Journal of Finance and Economics. 2019; 7(3):81-87. doi: 10.12691/jfe-7-3-1

### Abstract

How much to spend on an option contract is the main problem at the task of pricing options. This become more complex when it comes to projecting the future possible price of the option. This is attainable if one knows the probabilities of prices either increasing, decreasing or remaining the same. Every investor wishes to make profit on whatever amount they put in the stock exchange and thus the need for a good formula that give a very good approximations to the market prices. This paper aims at introducing the concept of pricing options by using numerical methods. In particular, we focus on the pricing of a European put option which lead us to having American put option curve using Trinomial lattice model. In Trinomial method, the concept of a random walk is used in the simulation of the path followed by the underlying stock price. The explicit price of the European put option is known. Therefore at the end of the paper, the numerical prices obtained by the Black Scholes equation will be compared to the numerical prices obtained using Trinomial and Binomial methods.

### References:

 [1] P Wilmott, JN Dewynne, and SD Howison. Option pric- ing, mathematical methods and computation, 1993. [2] Fischer Black, Michael C Jensen, Myron Scholes, et al. The capital asset pricing model: Some empirical tests. Studies in the theory of capital markets, 81(3):79-121, 1972. [3] Robert C Merton et al. Theory of rational option pricing. Theory of Valuation, pages 229-288, 1973. [4] John C Cox, Stephen A Ross, and Mark Rubinstein. Op- tion pricing: A simplified approach. Journal of financial Economics, 7(3): 229-263, 1979. [5] Phelim P Boyle. Options: A monte carlo approach. Jour- nal of financial economics, 4(3): 323-338, 1977. [6] Phelim P Boyle and Sok Hoon Lau. Bumping up against the barrier with the binomial method. The Journal of Derivatives, 1(4): 6-14, 1994. [7] Hu Xiaoping, Guo Jiafeng, Du Tao, Cui Lihua, and Cao Jie. Pricing options based on trinomial markov tree. Dis- crete Dynamics in Nature and Society, 2014, 2014. [8] F AitSahlia and Tze L Lai. Valuation of discrete barrier and hindsight options. Journal of Financial Engineering, 6(2): 169-177, 1997. [9] Harish S Bhat and Nitesh Kumar. Option pricing under a normal mixture distribution derived from the markov tree model. European Journal of Operational Research, 223(3):762-774, 2012. [10] XIONG Bing-zhong. A trinomial option pricing model based on bayesian markov chain monte carlo method. Journal of Jiaxing University, (6):9, 2012. [11] Fei Lung Yuen and Hailiang Yang. Pricing asian options and equity-indexed annuities with regime switching by the trinomial tree method. North American Actuarial Journal, 14(2): 256-272, 2010. [12] Paul Wilmott. The mathematics of financial derivatives: a student introduction. Cambridge University Press, 1995. [13] George Marsaglia et al. Evaluating the normal distribu- tion. Journal of Statistical Software, 11(4):1-7, 2004.