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

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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

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

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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