# What problems can be visualized in topographic finance? By Paul Cottrell

Three possible problem types can be visualized through topographic financial techniques, albeit this is not an exhaustive listing.  We will look at econometric problems first.  Econometric information can be very data intensive.  We need a means to be able to data mine and visualize these sorts of econometric problems.  One such three–dimensional dataset is unemployment, time, and gross domestic product.  By having all three factors in one graph will allow for easier analysis to be accomplished.  Another econometric problem is related to tax rates.  By using a Laffer curve we can see how tax rates can affect actual tax revenue.  But what if we wanted to understand tax rates and tax revenue over time?  We can accomplish this by using topographic finance.  A Laffer surface can be created, whereby the three dimensions are tax rate, time, and tax revenues.  By using this sort of economic analysis, with respect to tax rates, we can determine an optimized tax policy.

The second type of problem that topographical finance can solve is visualization of financial information.  In terms of fundamental analysis, financial ratios, balance sheets, and income statements can be visualized.  For example, price-to-earnings ratio, revenue growth rates, and time can be inputted into a three–dimensional graph to help compare different companies to determine if an investor should invest into that company.  Another example within the fundamental analysis domain is long–term debt, time, and earnings.  As can be imagined, there are countless configurations to graph financial problems.

Our third example is technical or quantitative financial problems.  We can utilize topographic finance by graphing price, time, and volatility; therefore allowing for an understanding of how volatility evolves through time and affects the price of an asset.  Another good example is the volatility surface for an option contract. When making a volatility surface for options strike price, time-to-maturity, and volatility are used.

Again, topographic finance can graph many different types of problems and will most likely evolve into utilizing hypercubes, whereby multiple three–dimensional spaces are compared with each other to understand high dimensional dynamics.  Many traders use lots of price charts with many indicators, which is utilizing hypercube faces to understand the dynamics of the market.