Until 1970, there was no single method for pricing an option. The value of option was mainly based on market sentiment. In this situation, traders who predicted an increase in the share price preferred call options more than traders who had a negative outlook on the underlying asset. Some market players used their own rules based on observations.
The model has some important simplifying assumptions about the world around us. However, in periods of imbalance and panic in the financial market, these assumptions are completely meaningless, which distorts the fair value of options. Read the “Intrinsic and time value of an option”.
According to the Black-Scholes model, the value of an option is determined on the basis of five factors:
In other articles we built binary tree model with three steps for the call option. Increasing the number of steps, i.e. reducing the time interval between steps, will lead to an absolutely similar result, which can be obtained by using Black-Scholes model, widely known in the financial industry.
The binary tree that was built in the article “Binary tree (Part I)” is a simplified form of the real option pricing model used by investment banks. The basic model assumes that the share price will either rise to $115 or fall to $85 during one period.
Due to the fact that an American option gives more rights than a European option, the value of an American option can never be lower than a European option. This does not mean that an American option should cost more.