2024-08-05 20:56:55

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A binomial tree is an order with 1 node, and the order is constructed with the help of two binomial trees, making it one or the other. It is used in valuing assets. Several binomial trees cover up to become binomial heaps of several values. It is an essential and useful tool when it comes to pricing. It is simple, making it both an advantage and a disadvantage simultaneously.

The binomial tree is easy to make and model out in a mechanical way, but the major problem lies in the values of the asset underlying it. In the binomial tree model, the asset can be only worth the two or possible values which is often non-realistic because the asset can be of any worth number of values in a given range. The binomial tree allows the investor to analyze when a value and its option can be exercised.

The option of assessing a value of high probability can be exercised only when the option has a positive value. There are many other ways that can be used in value, such as the black Scholes model, which is faster. But the binomial tree is considered the most credible and reliable one in assessing the values of the numbers.

## Properties of the binomial tree

A binomial tree has few properties. They are:

• It has 2k nodes.
• It has depth as K.
• There are kainic nodes at the depth.
• All the roots have the degree k.
• The order is from left to right in the way as k-1, k-2, and so on.
• Each node is calculated by multiplying the lower node, moving it to the upper side, and multiplying the presiding high code by the lower one.
• The main point in the calculation is it must give the same result.
• Another important property is the asset price begins with the node, which states the initial price and then divides the two nodes making one with the probable price of the underlying asset and the other in the future point. The asset price can go up or down based on the price from the mode of its origination.
• With the help of the binomial tree, it can value calls and put up options using the price which is most probable in the underlying movements of the asset.
• These properties can be undertaken and evaluated while using a binomial tree's help in assessing values.

## How is the binomial tree made?

Binomial trees can be easily made in excel sheets and also in normal ways. It is the best way to present the model in a visual mode. The use of binomial mode helps in showing the option payoff and probability at different modes. The node outlines the oaths of the price of the asset that underlines and can take ample time. It can be represented as a general one-period call option as well. One way is mentioned below:

It can be represented in the formula as well. One thing which has to be understood is that the put options use the same formula as the call option. The pie in the formula is the probability of a move, r is the rate of the discount rate, and in order to arrive at the probability of a move which is up, another formula is applied, which is :

On excel, the spreadsheet can be used to make the binomial tree calculations easier. It is quite flexible as it can accommodate the changing circumstances in variation, and therefore it makes a suitable way for evaluating early exit strategies. Coming to the Black Scholes model, they both have similar forms of results in evaluation where the viability is a binomial pricing option.

But there are limitations which remain in a way in which the future prices are not predicted properly. It becomes more tedious when there is a possibility in order to forecast the expected payoffs at the end of each period node. A lot of binomial trees make a binomial heap and cast out the pricing, and analyses the value to the maximum limits. The calculation can be based both on formulas and the excel sheet and can be time taking but is a lot more reliable.

## Binomial Trees Examples

An example can be taken where a particular stock and its year at present is \$. The ATM option has a strike price of \$ 50 within the given expiry time. There are two traders, John and Michael, and they both believe that either will rise to 60dollars or fall to 40 dollars in a year. They agreed on the expected price level in a given frame of a year, but there can be disagreement on the probability of going up and down. John believes it to be 60, which would be 60%, and Michael believes it to be 40, which is 40 per cent. Based on this, the price of the call option would be decided; this is how the binomial works.

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