# Alternative Approach for the Derivation of BlackScholes Partial Differential Equation in the Theory of Options Pricing Using Risk Neutral Binomial Process

Fadugba, S. E. and Okunlola, J. T. and Adeyemi, E. I. (2015) Alternative Approach for the Derivation of BlackScholes Partial Differential Equation in the Theory of Options Pricing Using Risk Neutral Binomial Process. Journal of Scientific Research & Reports, 4 (7). pp. 1-9. ISSN 2320-0227 Text Fadugba472014JSRR14349_1.pdf - Published Version Download (411kB)
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## Abstract

This paper presents a risk neutral binomial process as an alternative approach for the derivation of analytic pricing equation called “Black-Scholes Partial differential Equation” in the theory of option pricing. Binomial option pricing is a powerful technique that can be used to solve many complex optionpricing problems. In contrast to the Black-Scholes model and other option pricing models that require solutions to stochastic differential equations, the binomial model is mathematically simple. Binomial model is based on the assumption of no arbitrage. The assumption of no arbitrage implies that all risk-free investments earn the risk-free rate of return and no investment opportunity exists that requires zero amounts of investment but yield positive returns. We derive Black-Scholes partial differential equation using risk neutral binomial process. We also discuss the convergence of binomial model to the analytic pricing formula, the Black-Scholes model for pricing options. Binomial model has the Black-Scholes analytic formula as the limiting case as the number of steps tends to infinity. This model is much more capable of handling options with early exercise because it considers the cash flow at each time period rather than just the cash flows at expiration.

Item Type: Article American option; binomial model; black-scholes model; black-scholes partial differential equation; convergence; european option; vanilla option. Q Science > QA MathematicsQ Science > QC Physics Faculty of Engineering, Science and Mathematics > School of Physics Mr. Victor Sebiotimo 14 Mar 2019 00:00 14 Mar 2019 00:00 http://eprints.abuad.edu.ng/id/eprint/131

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