Comparing black-Scholes and binomial models for pricing call options

Price Call Models

Black-Scholes Model and the Binomial Model are some of the widely used price call options. Despite the fact that these two models share the same theoretical foundation and assumptions like the Brownian motion theory and risk neutral valuation, they happen to have some notable differences (Rendleman & Bartter, 1979).

The Black-Scholes model is basically used to calculate a theoretical call price. This call price ignores dividends paid during the life of the call option. Some of the determinants of the option price include stock price (S), strike price (X), volatility (v), time to expiration (t), and short-term interest rate (r) (Rendleman & Bartter, 1979). This model has got some assumptions. One of the assumptions is that the stock pays no dividend during the option's life. This assumption is a serious limitation of the model considering that companies do pay dividends to their shareholders (Rendleman & Bartter, 1979). The fear has always been that higher dividend yields would elicit lower call premiums. Discounted value of a future dividend has to be subtracted from the stock price to adjust the model. Black-Scholes model uses European exercise terms that dictate that an option can only be exercised on the expiration date. Compared to American exercise terms, Europeans terms are deemed inflexible. Nevertheless, this is not a major concern since very few calls are ever exercised before the last few days of their life. This model also assumes that the markets are efficient and therefore people cannot predict the direction of the market or an individual stock (Rendleman & Bartter, 1979).

Another assumption is that no commissions are charged even as it is public knowledge that participants pay commissions to buy or sell options. The fees paid by individual investors are deemed substantial to an extent that they can distort the output of the model. It is widely believed that interest rates remain constant and known and that returns are lognormally distributed. One major advantage with Black-Scholes model is that it is capable of letting you calculate a very large number of option prices within a limited period of time (Rendleman & Bartter, 1979). However, it cannot be used to accurately price call options with the American style exercise term that does not consider steps along the way.