Tail probability calibration
The inequality describes for various assets what the market is saying about probabilities of extreme events. This leads naturally to the question of whether the markets tend to be well-calibrated. We will try to determine this from historical data. It might be that the degree of calibratedness is sector dependent. We'll try to identify patterns.
Volatility measures
What we calculate, e.g. what the market is saying about the likelihood of a 50% drop in the value of a particular security is a measure of volatility. There are other measures of volatility and it seems quite natural to investigate the degree to which these various measures track one another.
Index tracker
The idea is to choose an index that closely simulates the world economy and track it. That is to say, to record its put options data, every day, for a sufficiently long time. This project differs from the current one in that we would need to slightly modify the program to extract and save the data we need to a file and have the server run the program, say, every day. Another program would compute desired statistics, averages for instance, and compare the currently searched stock symbol to the index. Furthermore, we would implement a graphical analysis to show the computational results.
Commodity POD
This is identical to the current project. We would just need to slightly modify the code to extract commodity Put Option Data and report on what markets are saying about commodities.
Treasury POD
This is also identical to the current project. We would need code to extract Put Option Data on US Treasuries and describe market pessimism about such bonds.
Currency POD
Put options on various currencies are readily available and are amenable to the same analysis.