Binomial Tree (Options) - Explained
What is a Binomial Tree?
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Table of ContentsWhat is a Binomial Tree?How Does a Binomial Tree Work?How is the Binomial Tree Used?Why Practitioners Prefer Binomial TreeBinomial Tree LimitationAcademic Research on Binomial Tree
What is a Binomial Tree?
In the finance field, the term binomial tree refers to a graphical representation with possible intrinsic values showing that an option may take place at different periods or nodes. Under this model, the options value depends on the underlying financial instruments, such as bonds or stock. On the other hand, the nodes option depends on the possibility that the underlying assets price will either increase or decrease at any particular node.
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How Does a Binomial Tree Work?
A binomial tree is an essential tool for those individuals who want to price embedded options and American options. The tree is simple to model; however, there when it comes to the possible values that the underlying asset can take within one period of time. The underlying asset can only be worth under a binomial tree model when there is precisely one out of the two possible values. Unfortunately, this is not realistic, because the worth of assets can take any given number value within a various range. Unlike other models, binomial option pricing has the capacity to handling a good number of conditions. For this reason, many individuals use this approach. The reason for this is that it is based on the underlying instruments description over some time and no single point. It is, therefore, used when valuing American options, which happen to be exercisable in a given interval and any time. The model is also used to do valuation of Bermudan options that are also exercisable given time instances.
How is the Binomial Tree Used?
You can use the binomial pricing model approach to trace the option keys underlying variables in discrete-time. You apply the binomial tree, also known as a lattice for several time steps between the expiration dates and valuation. Note that each node in the tree represents the underlying possible price at any given point in time. Valuation using a binomial tree is performed iteratively, begging at each the nodes that you can reach at the expiration time, and then compute backward through lattice towards the first valuation date (first node). Note that the value calculated at each stage becomes the options value at that particular time. When you do option valuation using a binomial tree, the process will take three steps, as shown below:
- Price tree generation
- Option values calculation at each final node
- Option values sequential computing at each preceding nod
Why Practitioners Prefer Binomial Tree
A binomial tree may be slightly slower being slower compared to the Black-Scholes formula but is more accurate, especially for longer-dated options on securities and dividend payments. It is for this reason that most practitioners prefer using the binomial models various versions in the options markets.
Binomial Tree Limitation
One major limitation of a binomial tree is that it may not be practical when it comes to some options. Note that some options have several uncertainty sources, while some have complicated features, making the binomial approach not fit for such. Monte Carlo simulation is the most preferred model when valuing these types of options. However, Monte Carlo simulation is time-consuming, making it not ideal for computing simulation with a small value of numbers.