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 article about synthetic forwards described the restrictions on option prices and a fundamental principle called put-call parity. The next logical step in the study of options and the Black-Scholes pricing model is the construction of a binary tree.

Binary option is one of the simplest types of exotic options. The owner of a binary option receives a fixed payoff if the price of the underlying asset is below or above a certain point at the time of expiry (or before) and receives no payout at all in all other cases.

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.

Trading binary options is a relatively recent phenomenon and represents an opportunity for those who love to invest and speculate on the stock markets, but at the same time carries huge risks for the trader. However, the concept of binary options has actually existed for several decades.

The option price consists of time value and intrinsic value. For call options, the intrinsic value is defined as the maximum of two numbers - zero and forward price of the underlying minus strike, for put options - zero and strike minus forward price of the asset.

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.