Monday, May 9, 2011

Greek Alphabet

No doubt about it, one area where a real-time simulation adds tremendous value is in the teaching of options.  Perhaps more than any other application of textbook finance, you really need analytics to make decisions and to appreciate the usefulness of the models.  

While there are many different exercises you can conduct, one of my favorites is one where students hedge the risk of a stock portfolio using index options, as described in our Hedging with Options real time project. We like using index options because we want to stress hedging on a portfolio-wide basis, not hedging individual securities by themselves (which would over-hedge the portfolio).

This introduces many concepts beyond basic option pricing and hedging: you have basis risk since you don’t have options on your portfolio, you need to understand correlations between the stocks (and whether these are stable), and of course you have to decide how to rebalance.  In this exercise, the equity positions don’t matter; the question is after you take the position, can you effectively hedge the price (and/or volatility) risk?  Variations of the project have options on smaller and larger equity indexes, and you really only need positions in one or two stocks to create an interesting problem.  As an extension, you could add index futures as well.  These types of projects also have the added advantage that to draw realistic conclusions on hedge performance, you only need a short period of time, say a week or two, so they fit in well into course timetables. 
In such a project, each student can use their own estimates of parameters (such as risk free rates and volatilities), though we provide default values.  All the analytics can also be calculated using implied volatilities.   In real time, you see both the individual and portfolio-level Greek parameters; aggregation is calculated using beta weightings, as done in practice and as explained in the project writeup.  There are three main analytic screens.  The first shows the Greeks at the portfolio level:


You can see the term “Implied” in parenthesis, this means that all the values are calculated using implied volatilities.   You can also use user-defined volatilities:

You can enter you own estimates (and these are then stored by the system) by clicking on Parameters; entering the numbers is easy, you can enter them one by one or you can copy and paste en masse from an Excel spreadsheet.
You can also see everything for each individual option, and as shown, export everything into Excel:

A second analytic shows you the volatility exposure; here is a screen shot of the volatility exposure of the position, you can also see this for every option individually:

So you can see what happens if there is a “non-local” shift in volatility.
The third analytic is the Value at Risk, so you can discuss tail behavior.  This is calculated using Monte Carlo simulation, and is shown at the portfolio level, by asset class, and by individual security.  Here is an example with two stocks and one option:

 What’s nice about these exercises is that it provides a very real way for students to see how the concepts and techniques are used.  Its hard to do this any other way.

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