Black-Scholes and Binomial Models

Black-Scholes and Binomial Model
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In the valuation of options there is arbitrage restrictions on valuing the options no matter the pricing approach used. The Binomial Model assumes that there is a single period with two dates expressing time 0 and time 1 which is the expiration or two periods. There are also perfect market assumptions for the Binomial Models. The Black- Scholes model is expressed as an equation with the main assumptions being that stock price volatility and the risk free interest rate are constant. The arbitrage-free Binomial Model incorporates different volatility assumptions, but to convert the Black Scholes model into the binomial model then one assumes that there is a multiplicative binomial process. Even though, the two approaches have different methods to value options they are based on the same fundamentals where there is no arbitrage in the risk-neutral valuation (Scialdone, 2007)
The Black-Scholes approach focuses on the stock price in pricing options, and as the stock price increases so does the call option, but the put option decreases holding other factors constant. The Binomial Model also assumes that stock prices have no role in determining the option pricing highlighting that the approach follows risk neutrality. Even though both pricing options calculate with the stock price being constant, the stock price movement is immaterial in valuing options highlighting the benefits of the approach.
In the Black-Scholes method the exercise and stock price are closely related and move in the same direction. Equally, the binomial model takes into account the exercise price in valuing options, but it also considers the likely effect of an early exercise (Nwozo & Fadugba, 2014). Consequently, the binomial model is better suited for the American option type which is more co...