You have seen that option pricing models let you quantify the risks of an option, and therefore of an option position. The risk measures we have talked about so far are really local measures. For example, the delta tells you the effect of a small change in the price of the underlying asset. Recently, a more global measure of risk has been proposed, called Value at Risk.

Option Tutor's Risk Management subject is about managing portfolio risk. In fact, you can manage an actual position using this subject, and even link it to real-time data.

We next describe the risk-management concepts, and then show you how to use Option Tutor to manage an option position.

Consider a portfolio of puts, calls, and futures. When you bring up the Risk Management subject, a new type of window, in which you can enter your portfolio appears:

You have to enter the basic parameters, and quantities, for puts, calls, and futures. You can have up to 25 puts, 25 calls, and 15 futures contracts. Here, we will use the default data set.

Tutor Note: Option Tutor checks to see how many options you have defined by scanning the strike price column. If a strike price is left blank, it assumes that you have not entered any data beyond that. Therefore, when entering data, do not leave blank lines, especially in the strike price column (and delivery price column for futures).

After you have entered the basic information, set a quantity and plot the exposure. Below the graphical display, you will see:

You can plot the value of the option as a function of either the underlying asset of the volatility of the underlying. When you do the former, the range of the underlying is taken from the graphical display window. You can change the range simply by typing in a new range, as illustrated below. The volatility exposure is calculated by perturbing the volatility of each option. Note that you can have a different volatility for each option. (You can also transfer the data easily into the option calculator or into the spreadsheet link to perform any calculations you want).

Besides the price/volatility exposures, you can choose a "payoff diagram" or a "profit diagram" The payoff diagram simply shows you the portfolio value. The profit diagram shows you the portfolio value minus the cost of acquiring the portfolio.

Tutor Notes:

• The program calculates the option values based on the model, not based on the market price. If you want to make these equal, you must recalculate the implied volatilities so that the market price and model prices coincide. To do this, transfer the data into Spreadsheet Link, calculate implied volatilities, and update volatilities here from the Transfer menu of Spreadsheet Link.
• For American options, you have a choice of computation method. The default is set at the analytic approximation, and you can also choose the trinomial model. Note that for some of the calculations, such as calculating value at risk, choosing the trinomial model with 500 steps can take quite a long time. We recommend that you step up to this, based on the speed of your computer.
• Besides looking at your portfolio value and exposure today, you can scroll it forward through time. Simply move the scroll bar. This gives you a very dynamic feel for how the exposure or the risk distribution changes.

Consider the default data set with 1 unit of the underlying asset. The profit exposure diagram is obtained by entering 1 for the quantity of the underlying and by selecting profit diagram:

and

Click on Plot Exposure (in the portfolio window) to get:

Tutor Note: From the X-axis of this display, you can see that we are doing calculations when the underlying ranges between 0 and 100. You can change this by typing in a new value and pressing the enter key.

In the portfolio window, let us buy 1 40-put, and re-plot the exposure:

Our exposure is:

Note how the old line remains on the screen. This way, you can compare different positions. The refresh button erases old lines.

You can see the effect of adding the put. Note also how the graph is "curved," unlike a terminal payoff diagram. This is because the calculations are being done today, not when the option matures. You can see the terminal payoffs by scrolling forward through time; some exercises in later chapters show you how to use this effectively.

You can also see the portfolio hedge parameters:

Your delta is positive, which means that you would benefit from an increase in the price of the underlying asset. If you want to be delta neutral (i.e. have a zero delta), you may want to buy some more puts. Similarly, by choosing quantities of options and futures, you can make your portfolio have whatever characteristics you want.

As stated previously, the Greek parameters shown are local measures of risk. You may also be interested in what happens to your portfolio if there is a large change in the price of the underlying asset. The measure called Value at Risk (VaR) is one way to measure this.

Here is how it works. Suppose the stock price is log-normally distributed (as in the Black-Scholes model), and has a volatility of 25% (this may be different from the implied volatilities you use for different options!). From the stock price distribution, we can randomly draw values of the stock. We do not need to know the drift rate of the stock if we only look at changes in the stock price from its current level.

For each stock price change, we can recalculate the value of our option portfolio. If we do this say a thousand times or ten thousand times, we get a distribution of portfolio values, which we call the "risk distribution." We can look at the "tails" of this distribution to get an idea of what the worst-case possibilities are. For example, we may want to know: what is the worst thing that can happen with 95% probability? This is the same as asking: what is the portfolio value such that 95% of the simulated values lie above it? You can also use a 90% cutoff or a 99% cutoff. The resulting number is called the VaR.

Option Tutor lets you do these (fairly complex) calculations quite easily. You have to specify a portfolio, as before, and the following additional information in the risk management subject:

On the right side of this, you can select the number of simulations, set the volatility of the underlying security, look at daily or weekly or monthly simulations, select the cutoff level, and finally, the number of days in the year! (This last one is useful if you want to distinguish between calendar days and trading days; there are typically about 260 trading days in a year).

Now, click Simulate in the portfolio window:

For 1 underlying and 1 40-put, we got the following risk distribution:

and found that 95% of the values exceed 49.5511. Every time you click simulate, you will get a new simulation.

The Risk Management subject of Option Tutor lets you evaluate the risk of a position using market data. There are different ways in which you can obtain market data:

• From the financial press, e.g., the Wall Street Journal or Investor's Business Daily
• From Internet sources, such as CNNfn.com
• From a live data feed, such as Reuters or Dow Jones-Telerate or another data source.

In the first two cases, you can enter market prices either by copying or pasting them in or typing them in. You can type these into the Market Price column of the portfolio window. To recalculate all the implied volatilities, bring up the Spreadsheet Link, and from the Transfer menu, get the portfolio from Risk Management, then calculate implied volatilities, and finally update the volatilities:

Even if you are using newspaper of Internet data, you may want to use the real-time data link and Excel to manage your data. Simply follow the directions for Excel below. The Real-Time Link lets Option Tutor read data directly from the data feed.

Select Real-Time Link from the menu of the portfolio window:

This brings up:

You have to specify how the program gets the data. We now step through this in some detail. We first explain what information you need, and then show you the procedure for some specific data sources. Note that you only have to specify this information once. You can then save it to a file (or in a spreadsheet), and then re-use it any time you want simply by reading it back in (or pasting it back in from a spreadsheet).

The Information:

1. Excel: First, if you can get real-time (or delayed data) into an Excel spreadsheet, then you are all set. Option Tutor can read it in directly from Excel. In fact, even if you are typing in data from a newspaper, the Excel link provides a very convenient way of managing your data.
2. A data source application: Option Tutor can receive information through what is called Dynamic Data Exchange (or DDE) in Windows. For such a data exchange, your data source application must be running on your computer and Option Tutor must be running on your computer. For example, Reuters has an application called the Data Dictionary, which runs under Windows. The Bridge information service has an application called the Bridge Data Exchange (BDE) while Telerate has the TwinDDE application.

Suppose you have the data in an Excel spreadsheet. (This could be a spreadsheet that updates data in real-time or it could be one in which you have simply typed in the data). This includes information on the price of the underlying asset, and the market quotes of all the options and futures in your portfolio.

What you need to do is to tell Option Tutor where the data are kept. For Excel, you have to tell it the name of the spreadsheet and connect each security with the cell in the spreadsheet. We first describe how you set up the data in gory detail; then, we how you how Option Tutor can read in the data quite easily if you follow a pre-specified format.

The Link Topic is where you tell Option Tutor that your are getting data from an Excel spreadsheet. Suppose your spreadsheet is called Book1 (which is the default name for a spreadsheet in Excel). Then, the Link Topic is Excel|Book1. Note the "pipe" character separating Excel and Book1; this typically appears on your keyboard as two vertical half-lines.

The Link Delay tells Option Tutor how long to wait before giving up on the data. This is specified in tenths of a second. The default value is 50 (or 5 seconds), which should be adequate for most applications.

The Link Topic and Link Delay apply to all the data. Next, you must tell Option Tutor which cell in the spreadsheet has what data. This information is given as the "Underlying Code" for the underlying and "Price Code" for the options and futures. Suppose the underlying is in Row 1 Column 2 of the spreadsheet; then the underlying code is R1C2. Suppose the first put option is in Row 2, Column 2. Then, the price code for the first put is R2C2. And so on.

The Format menu item sets up a default format. For Excel, the default link topic is Excel|Book1, the underlying is in R1C2, the puts are next, also in column 2, followed by the calls, and finally the futures. The order follows the derivatives you defined in the portfolio in the Risk-Management subject. If you keep your data in this format, linking becomes easy; you simply select Excel from the Format menu. Otherwise, you can use this as a template and then change the fields as appropriate.

Note: the information in this section may be different, depending on your installation. Please contact your computing support staff or the data feed provider for up to data information.

The easiest way to link to Reuters or Telerate is to specify the name by which the data feed refers to the security and to then let Option Tutor set the codes for you. We provide a detailed example for linking with Reuters; those for Telerate (or other data sources) are similar; you simply have to change the codes appropriately.

Consider S&P500 index options in Reuters. The code for the S&P500 index is .SPX. The following are names of options in the Reuters system:

SPX690L.W
SPX700L.W
SPX710L.W
SPX690X.W
SPX700X.W
SPX710X.W

The first 3 are puts (indicated by the letter L in the code), the next three are calls, and the Reuters code for the Chicago Board of Options Exchange (CBOE), where these options are traded, is W (which accounts for the .W at the end). The strike prices are shown (at the time of this writing, the S&P500 index stood at approximately 700).

For Reuters, the link topic is REUTER|IDN (while for Telerate, it is TWINDDE|QFRecord).

This is all you need to know. Now, enter these into the Name fields, as shown (NOT in the Code field):

Next, simply select Reuters from the Format menu, and the program fills in the link topic and price codes for you:

Note how Option Tutor picked the LAST field for the codes. This is the default setting. Usually, you can replace LAST with BID for the bid price and ASK for the ask price (if the security is not an index!).

Tutor Note: The names are only needed if you are using the Format menu to set up the codes. If you know the codes, you can simply type in the codes are proceed.

Once Option Tutor knows the Link Topic and the various codes, it is ready to receive real-time data. You can choose between a Manual Link and an Automatic Link. In a manual link, you have to click the Manual Update button to update data. In an automatic link, prices are updated whenever they change.

If you select Automatic Data Transfer, then the market prices are transferred to the Risk Management subject whenever they change. With a manual link, they are transferred whenever you update; with an automatic link, whenever a price changes.

One reason you want to link to real-time data is to update the implied volatilities of the options. This lets you study the portfolio Greeks, the exposure profile, and VaR with up to data information. You can choose Automatically Recalc Vols to re-compute implied volatilities whenever prices change.

Finally, you can choose to have either the exposure profile or the Var simulation re-computed whenever prices change by selecting Automatic Replot. What is re-plotted depends on the last thing you plotted in Risk Management.

Tutor Note: Automatic re-plotting can be quite computer intensive, so be careful when you switch this on. This is particularly true for the VaR calculations with American options and many simulations.