The value of an option is estimated using several variables used in different option pricing models such as Black-Scholes and Binomial. The variable affects the value of an option in various ways depending on the type of option. The variables that influence the pricing of an option in the Black-Scholes and Binomial models are compared below together with other attributes in them.
Both Binomial and Black-Scholes Models use the prices of the underlying stock to get the prices of the option. The changes in the underlying security prices in the both models affect the prices of the option. For example, a rise in the price of the stock leads to increase in the call option. An assumption that underlying stock price follows a normal distribution and follows stochastic process is put forwards in both models. The underlying stock prices are also assumed to have no negative prices. The two models find the present value of the option price considering the time to expiry and the price of the underlying stock. They also use risk-free rate in the determination of the current value of the option. The models assume that firms operate in a frictionless market where there are transaction costs and no taxes charged. The models assume that the investors are risk neutral.
Binomial model calculates the value of an option at every point of its life. It breaks down the time to expiry into different steps resulting in different values at every value. The time breakdown makes it a better model to value an American option, unlike Black-Scholes model that assume a continuous to expiry time. Black-Scholes calculates one value of the option from the present period to the period of expiry considering factors affecting the price of the option such as risk-free rate remains the same for the period. The Binomial model can value and option at any point when the holder wants to exercise it while Black-Scholes assumes options are only exercises at the end of expiry period. The Binomial model in every step provides two values; the up-price and the down-price giving an investor a chance determine the price in difference scenarios. It also considers some factors ignored by Black-Scholes such as dividends. Since, if they are paid at a particular point they are considered in the calculation of the value of the option.
Calculation of option price using Black-Scholes model is fast and takes a single estimate. On the other hand, using Binomial model in the calculation of options is slow. The process involves several processes where each has two considerations making it a long one. Unlike Black-Scholes that calculates a single value, the Binomial model assumes the probability of each point taking place resulting in different values. The continuous nature of the Black-Scholes model uses the same risk-free rate over the option period while the Binomial model uses several rates that vary from one point in time to the other. The difference in the rates enables one to have numerical values using a Binomial model where the Black-Scholes gives a general explanation.
The Binomial Option Pricing model uses simple mathematical calculations breaking time into short periods. The calculations are not complex, and an ordinary finance student can use it in the determination of the value of an option. On the other hand, the Black-Scholes model uses a complicated mathematical formula that is beyond the financial analyst. The method employs sophisticated mathematics calculations that an ordinary economic student may find difficult to use.
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