On a Class of Equity Models for the Valuation of the European Call Options

Fadugba Sunday Emmanuel; Ajayi Adedoyin Olayinka

doi:https://doi.org/10.14445/22315373/IJMTT-V26P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 26 | Number 1 | Year 2015 | Article Id. IJMTT-V26P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V26P504

On a Class of Equity Models for the Valuation of the European Call Options

Fadugba Sunday Emmanuel, Ajayi Adedoyin Olayinka

Citation :

Fadugba Sunday Emmanuel, Ajayi Adedoyin Olayinka, "On a Class of Equity Models for the Valuation of the European Call Options," International Journal of Mathematics Trends and Technology (IJMTT), vol. 26, no. 1, pp. 13-19, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V26P504

Abstract

This paper presents binomial and the Leisen-Reimer models for the valuation of the European call option. Binomial model is an iterative solution that models the price evolution over the whole option validity period. This model is a powerful technique that can be used to solve the Black-Scholes partial differential equation and other complex option-pricing models that require solutions of stochastic differential equations. Leisen-Reimer model is a technique that modifies the parameters of the binomial tree to minimize the oscillating behaviour of the value function. We compare the call prices via the two equity models in the context of the Black-Scholes model. The numerical result shows how convergence changes as the number of steps in the binomial calculation increases as we vary the underlying asset price. We also observe that the Leisen-Reimer model removes the oscillation and produces estimates close to the analytic option valuation formula “the Black- Scholes model” using only a small number of steps.

Keywords

We also observe that the Leisen-Reimer model removes the oscillation and produces estimates close to the analytic option valuation formula “the Black- Scholes model” using only a small number of steps.

References

[1] F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, 81, pp. 637-654, 1973.
[2]J. Cox, S. Ross and M. Rubinstein, “Option pricing: A simplified approach,” Journal of Financial Economics, 7, pp. 229-263, 1979.
[3] J. Hull, Options, “Futures and other derivatives,” Pearson Education Inc. Fifth Edition, Prentice Hall, New Jersey, 2003.
[4] D. Leisen, and M. Reimer, “Binomial models for option valuation - Examining and improving Convergence,” Applied Mathematical Finance, 3, pp. 319-346, 1996.
[5] C.R. Nwozo and S. E. Fadugba, “Some numerical methods for options valuation,” Communications in Mathematical Finance, 1, pp. 57-74, 2012.
[6] C.R. Nwozo and S. E. Fadugba, “Monte Carlo method for pricing some path dependent options,” International Journal of Applied Mathematics, 25, pp. 763-778, 2012.
[7] C.R. Nwozo and S.E. Fadugba, “On the accuracy of binomial model for the valuation of standard options with dividend yield in the context of Black-Scholes model”, IAENG International Journal of Applied Mathematics, 44, pp. 33-44, 2014.
[8] Y. Tian, “A Modified Lattice Approach to Option Pricing”, Journal of Future Markets, 13, pp. 563-577, 1993.
[9]Wallner C. and Wystup C. “Efficient Computation of Option Price Sensitivities for Options of American Style,” Business School of Finance and Management, Centre for Practical Quantitative Finance, pp. 1-31, 2004.