You are the fortunate owner of some asset, such as shares of stock in a Fortune 500 company, a quantity of some precious metal like gold, some currency like Euros, and lately you've been hearing from the financial news concerns about where the market is headed. We are constantly bombarded with warnings about the relative health of the economy as market watchers draw your attention to a host of relevant indicators, the gross national product, the unemployment rate, the consumer price index, housing starts, employment, inventories, the weather, etc. ... the list seems to go on and on.
At a given point in time with all of these sources of information, it would be nice to be able to quantify market pessimism, especially about the particular asset you are holding, and do it in a way that is easily understood. The purpose of this project is to describe and quantify market pessimism about assets using the prices of put options on them. The methodology described here generalizes in various ways to give metrics for market pessimism about broad categories of assets.
The idea we work with is quite simple. Under market equilibrium, when the price of a put option on an asset stabilizes in the market to some value, the market is implicitly expressing its beliefs about the probability that the asset value will fall to below some value. In fact, we demonstrate the following key result upon which this work is based:
If the price of a put option on the asset is p, the strike price of the option is K, and the expiration date of the option is at date T, then the market is saying that the probability of the asset falling in value below K before T is at least p/K.
This inequality was discovered (no doubt rediscovered!) by Daniel Q. Naiman, Professor and Chair in the Department of Applied Mathematics and Statistics in the Whiting School of Engineering at Johns Hopkins University. The idea of even considering such a result was inspired by a financial analyst speaking at Johns Hopkins who mentioned the strategy of hedge fund managers selling way out of the money put options in order to improve their alpha. If the market is willing to buy such put options it must believe, in a collective sense, that the probability of landing in the money is sufficiently high to justify the investment. In the process the market is informing investors of its current level of pessimism in a simple quantifiable manner.
At the time (Fall 2007) Naiman was teaching a course called Introduction to Financial Mathematics, and mentioned to his class the idea of a website in which market pessimism about assets could be demonstrated in real-time. The idea was to allow visitors to this site to enter an asset of their choosing (it has to be one with an options market). The site would download option prices from the internet and provide a table with probability bounds.
Charles Dean and Amanuel Alemu were students in the class at the time and became interested in the idea. Thanks to the combined efforts of Charles, Amanuel, and Dan during Spring 2008, this site came to fruition. Visitors can now check the degree of market pessimism about any NYSE stock or index for which options are traded.
Winston Churchill once said:
"This is not the end. It is not even the beginning of the end. But it is, perhaps, the end of the beginning."
We're just getting started. There are many more ideas to pursue.