Comparison: Binomial model and Black Scholes model

Amir Ahmad Dar; N. Anuradha; Amir Ahmad Dar; N. Anuradha

doi:10.3934/QFE.2018.1.230

Quantitative Finance and Economics

2018, Volume 2, Issue 1: 230-245. doi: 10.3934/QFE.2018.1.230

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Research article

Comparison: Binomial model and Black Scholes model

Amir Ahmad Dar ^{1
,
,},
N. Anuradha ²

1.
Department of Mathematics and Actuarial Science, B S Abdur Rahman Crescent University, IN
2.
Department of Management Studies, B S Abdur Rahman Crescent University, IN

Received: 26 October 2017 Accepted: 24 December 2017 Published: 13 March 2018
JEL Codes: G12

The Binomial Model and the Black Scholes Model are the popular methods that are used to solve the option pricing problems. Binomial Model is a simple statistical method and Black Scholes model requires a solution of a stochastic differential equation. Pricing of European call and a put option is a very difficult method used by actuaries. The main goal of this study is to differentiate the Binominal model and the Black Scholes model by using two statistical model -t-test and Tukey model at one period. Finally, the result showed that there is no significant difference between the means of the European options by using the above two models.
- European options,
- Binominal model,
- Black Scholes model,
- t-test,
- Tukey model
Citation: Amir Ahmad Dar, N. Anuradha. Comparison: Binomial model and Black Scholes model[J]. Quantitative Finance and Economics, 2018, 2(1): 230-245. doi: 10.3934/QFE.2018.1.230

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Abstract

The Binomial Model and the Black Scholes Model are the popular methods that are used to solve the option pricing problems. Binomial Model is a simple statistical method and Black Scholes model requires a solution of a stochastic differential equation. Pricing of European call and a put option is a very difficult method used by actuaries. The main goal of this study is to differentiate the Binominal model and the Black Scholes model by using two statistical model -t-test and Tukey model at one period. Finally, the result showed that there is no significant difference between the means of the European options by using the above two models.

References

[1]	Baxter M, Rennie A (1996) Financial calculus: an introduction to derivative pricing. Cambridge university press.
[2]	Blattberg RC, Gonedes NJ (1974) A comparison of the stable and student distributions as statistical models for stock prices. J Bus 47: 244–280. doi: 10.1086/295634
[3]	Boyle PP (1977) Options: A monte Carlo approach. J Financ Econ 4: 323–338. doi: 10.1016/0304-405X(77)90005-8
[4]	Carlsson C, Fullér R (2003) A fuzzy approach to real option valuation. Fuzzy sets systems 139: 297–312.
[5]	Cox JC, Ross SA (1976) The valuation of options for alternative stochastic processes. J Financ Econ 3: 145–166. doi: 10.1016/0304-405X(76)90023-4
[6]	Cox JC, Ross SA, Rubinstein M (1979) Option pricing: A simplified approach. J Financ Econ 7: 229–263. doi: 10.1016/0304-405X(79)90015-1
[7]	Feng Y, Clerence CYK (2012) Connecting Binominal and Back Scholes option pricing modes: A spreadsheet-based illustration. Spreadsheets Education (eJSIE), vo. 5, issue 3, article 2.
[8]	Fama EF (1965) The behaviour of stock-market prices. J Bus 38: 34–105. doi: 10.1086/294743
[9]	Hull JC (2006) Options, futures, and other derivatives. Pearson Education India.
[10]	Hull J, White A (1987) The pricing of options on assets with stochastic volatilities. J Financ 42: 281–300.
[11]	Ingersoll JE (1976) A theoretical and empirical investigation of the dual purpose funds: An application of contingent-claims analysis. J Financ Econ 3: 83–123. doi: 10.1016/0304-405X(76)90021-0
[12]	Liu SX, Chen Y (2009) Application of fuzzy theory to binomial option pricing model. In Fuzzy Information and Engineering (pp. 63-70). Springer, Berlin, Heidelberg.
[13]	Merton RC (1973) Theory of rational option pricing. Bell J Econ manage science 4: 141–183. doi: 10.2307/3003143
[14]	Dar AA, Anuradha N (2017) Probability Default in Black Scholes Formula: A Qualitative Study. J Bus Econ Dev 2: 99–106.
[15]	Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Political Econ 81: 637–654. doi: 10.1086/260062
[16]	Dar AA, Anuradha N (2017) One Period Binomial Model: The risk-neutral probability measure assumption and the state price deflator approach.
[17]	Mandelbrot B (1963) The variation of certain speculative prices. J Bus 36: 394–419. doi: 10.1086/294632
[18]	Nargunam R, Anuradha N (2017) Market efficiency of gold exchange-traded funds in India. Financ Innov 3: 14. doi: 10.1186/s40854-017-0064-y
[19]	Oduro FT (2012) The Binomial and Black-Scholes Option Pricing Models: A Pedagogical Review with VBA Implementation. Int J Bus Inf Technology 2.
[20]	Lazarova L, Jolevska-Tuneska B, Atanasova-Pacemska T (2014) Comparing the binomial model and the Black-Scholes model for options pricing. Yearb Fac Computer Science 3: 83–87.
[21]	Dar AA, Anuradha N (2017) Use of orthogonal arrays and design of experiment via Taguchi L9 method in probability of default.
[22]	Liang J, Yin H-M, Chen X, et al. (2017) On a Corporate Bond Pricing Model with Credit Rating Migration Risksand Stochastic Interest Rate.

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