Motivating Question:

How can visualizing the binomial pricing model with European and American-style call and put options aid in the understanding of option valuation? How can the visualization further the development of intuition with regard to the impact on pricing of the various determinants of valuation (model parameters)?

Data Sources:

Given the theoretical nature of the proposed visualization, empirical data is not utilized in the modeling process. Users are instead prompted to provide parameter inputs, which are used to generate the displays. The concepts underlying the visualizations are outlined in Options, Future, and other Derivatives, by John Hull.

Design and Features:

The visualization consists of two primary display areas. The top area consists of user input fields allowing the editing and submission of changes to model parameters. The bottom area displays the model output in the form of a node-graph representation.

I allow users to fully customize model inputs (implementation as text fields) in order to make the model generalizable to any option pricing scenario, and to allow users to essentially play around with model inputs towards developing an intuitive (visualizing pricing data encoded by length) understanding of the dynamics underlying the binomial pricing model. Furthermore, the model allows for the pricing of both call and put options, as well as both European (no early-exercise) and American (early-exercise) options, encompassing the totality of possible non-exotic option styles. I allow for the extension of the model to multiple time periods via a slider object, to allow users to visualize the binomial model across varying time horizons (increasing depth of pricing node-graph).

I allow users to view the graph-node representation of the underlying security prices, the option prices, as well as the change from the original in order to better distinguish trends across the graph. I also provide a binomial volatility matching utility so as to facilitate the representation of options on real underlying securities based on market data.

Instructions:

To initialize the visualization using the default option parameters, simply click the “submit parameters” button. The number of time periods can be changed dynamically (not using the “submit parameters” button) by adjusting the slider.

Click on one of the tabs above the model display area to view either the evolution of the underlying security’s price (default), of the option’s price, or of the change in either the underlying’s or the security’s price in order to better distinguish differences between length encodings of model output values. Click the "toggle values" button to toggle the view of the individual nodes/bars' values on/off.

To edit model parameters, simply enter in a valid float in any of the text input fields, or to change the option style, click on one of the respective radio buttons. Click the “submit parameters” button when finished editing and the visualization will update accordingly. Note that the “binomial volatility matching” tab above the output area will display a utility that allows the mapping of security volatility to corresponding up and down states to facilitate the application of the model to real underlying securities. Simply input the relevant data into the utility and subsequently input the corresponding uptick and downtick multpliers as inputs.