A binomial tree is a graphical representation of a scenario with two possible outcomes at each stage, commonly used in finance to track asset price movements and evaluate call and put options. The binomial option pricing model uses a formula based on the Black-Scholes model to determine the value of an option, but the assumptions of both models make them less relevant to real-life situations.
A graphical representation of a scenario with two possible outcomes at each stage, a binomial tree is basically a tree diagram starting with one node that leads to two more nodes which could each lead to two more nodes, and so on. In finance, a binomial tree can track asset price movements. A binomial tree is also ideal for evaluating call and put options, because investors either lose or win, so there are always two possible outcomes.
A binomial tree for asset prices begins with a node indicating the initial price of the asset, then splits into two nodes, each with a likely underlying asset price at some future point in time. The price of the asset can go up or down relative to the price at the source node. The investor can create a binomial tree that plots likely asset price movements at different time points. The binomial tree can also value call and put options using the likely price movements of the underlying asset.
Call and put options are related to an underlying asset, which could be stocks, futures or commodities. At all times, the value of an option depends on the price of the underlying asset. Call and put options have a strike price and the investor earns profits or suffers losses depending on whether the price of the underlying asset on the expiration date is above or below the strike price.
Also known as the binomial option pricing model, the binomial tree pricing call and put options uses a formula based on the Black-Scholes model to determine the value of an option at any time before its expiration date. The Black-Scholes model helps investors determine whether the current option price is at its fair value, overvalued, or undervalued. To calculate the option value, the investor needs to know the initial asset and option prices, the option strike price, the time remaining to expiration, the volatility, the risk-free rate of return and the interest rate.
The fundamental problem with a binomial tree is that it assumes that the price of the underlying asset can only be one value or another value; in fact, it can be any value. The Black-Scholes model also has assumptions including that the asset pays no dividends, the options are European options that can only be exercised on the expiration date, the investor pays no fees, interest rates remain constant, and volatility remains constant. These assumptions make the binomial tree less relevant to real-life situations.
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