Skew Parameters

To modify a volatility skew, select Skew Parameters from the Volatility Skew menu. Selecting Skew Parameters displays the Volatility Skew dialog.

The Volatility Skew menu consists of two sections. Were you to split the skew parameters menu approximately in half, you would separate the two sections. The first section defines which options make up the skew. The second section defines how the skew is calculated.

The First Section

The first section consists of the following fields.

Field

Function

Symbol

Specifies the underlying instrument used in calculating the volatility skew.

Calls

Toggles calculation of calls on and off.

Puts

Toggles calculation of puts on and off.

Rollover

Causes the skew to rollover upon contract expiration.

Extend

Enables you to create a skew on nearer-month underlying instruments which can be applied to more distant option expirations.

Name

Specifies the name of the volatility skew. This name identifies the skew in your database.

Expiration Switch

(This field has no heading.) Enables you to include or suppress the instruments that the different option expiration chain used in creating the skew. This toggle is an asterisk. If the asterisk is visible, the instrument is included. If the asterisk is not visible, the instrument record is shaded gray and suppressed.

Month

Identifies expiration month.

Dots

Toggles the display of dots in the skew.

Line

Toggles the display of a line in the skew.

Xdays

Displays the number of days until the option expires.

Uprice

Displays the price of the underlying instrument.

Base

Enables you to enter a base for evaluating short term interest rate futures (i.e., Eurodollars and Treasury Bills).

Dividend Type

The dividend type field has no label. It is only displayed if the underlying instrument is an index or stock, and it appears next to the xDate (or Yield) field. Selecting the Dividend Type field displays the Dividend Type menu. Selecting an item from this menu enables you to define schedule on which distributions occur.

Selection	Function
None	No dividends.
Quarterly	Dividends occur quarterly. The last known dividend amount automatically serves as the dividend amount for all future distributions.
Semiannual	Dividends occur semi-annually. The last known dividend amount automatically serves as the dividend amount for all future distributions.
Annual	Dividends occur annually. The last known dividend amount automatically serves as the dividend amount for all future distributions.
Discrete	Only known dividends are included in the calculation. No assumptions are made about future dividends.
Yield	Annualized dividend yield.

Yield

If the underlying instrument is an index or stock, the Yield field is displayed to the right of the expiration table. This field enables you to enter the annualized dividend yield.

Div xDate

Enables you to define the dividend amounts distribution dates. This field is displayed only if the underlying instrument is an index or stock, and it is displayed to the right of the expiration table. Selecting this field displays the Dividend menu, which enables you to enter dividend amounts and a distribution dates.

The first dividend amount and distribution date automatically passes to the Div and xDate fields, respectively.

A skew definition consists of information derived from these fields. How you define a skew depends on how you want to apply the skew. A skew can be straight forward (a skew on a future's lead month contract applied to lead month options) or more dynamic (a skew on a future's first out month contract that rolls over at expiration applied to out-month options, which trade too sparsely to produce a valid skew). By itself, a skew is an important perspective on volatility, but how you define a skew or, how you intend to apply it is even more important.

The fields in the definition section derive default values from the technique you used to enter an instrument in the volatility skew window. As mentioned above, there are four techniques for entering a symbol in a volatility skew menu. Regardless of which technique you use, the characters you type are displayed in the Symbol Field.

The Symbol Field

The symbol field contains the instrument symbol you entered in the volatility skew window. How you enter a symbol is important. The following table summarizes symbol entry nuances.

Entry

Example

Function

<index_symbol>

<stock_symbol>

<future_symbol_root>

OEX

IBM

Displays all calls and puts on the future, index or stock for all expirations.

<future_symbol_root>+<expire_month>+<expire_year>

USM5

USM5 Displays all calls and puts on the future expiration you specify (no extension or rollover).

<symbol_root> + <wildcard>

<index_symbol> + <wildcard>

<stock_symbol> + <wildcard>

US#

OEX#

IBM#

Displays all calls, puts, on the expiration specified by the wildcard and sets up the skew parameters to rollover at expiration. The wildcard differentiates a future from a stock when the stock has a symbol that is identical to the future's symbol root.

If you enter an index symbol, a stock symbol, or a future symbol root, you create an option expiration chain. An option expiration chain is a table of the all the expirations of the options on an underlying. If you enter a future symbol with a specific month and year code, the resulting chain contains only options on that future.

Entering a symbol (regardless of the method you use) in a skew window populates the fields in the definition section of the Volatility Skew dialog box. Depending on the type of symbol you enter, other fields may show up in the definition section. If you enter a stock, index, or foreign exchange instrument, fields for dividends and dividend dates, yields, or foreign interest rate, respectively, will appear. The Dividend menu is exactly same menu that comes up in options charts.

The wildcard is the number sign (#). The wildcard can be appended to a future symbol root to differentiate it from an identical stock symbol. The wildcard also turns on the rollover toggle.

Expiration Chains

An expiration chain is the table listing the different expirations for an option market. It varies in total rows depending on the number of option expirations listed on the instrument. The Table contains the following fields:

Field	Function
Month	Enables you to suppress and edit individual volatility values.
Dots	Renders the respective option expiration using dots.
Line	Renders the respective option expiration using a line.
Expiration Switch	Toggles the display of the respective option expiration on and off. Set to on, the option expiration plays a role in calculating the skew. Set to off, the option expiration is ignored by the skew.
Xdays	Displays the number of days to expiration.
Uprice	Displays the price of the underlying instrument.
Base	Enables you to enter a base for evaluating short term interest rate futures (i.e., Eurodollars and Treasury Bills).

You can use the dots and line rendering methods together or separately, but be careful not to turn them both off. Turning both rendering methods off will suppress the option expiration from the skew window.

The Expiration Switch

The expiration switch (which has no heading) is also a toggle. It determines whether a particular option expiration is displayed in a skew window. Set to on, the respective expiration is rendered in white, and an asterisk indicates the switch is on. Set to off, the asterisk disappears, and the record is rendered in gray.

Apart from the obvious effect of making a particular option expiration display in a skew window, the expiration switch has another significant roles: it determines whether an option expiration is included in the skew curve calculation. Further, if you turn on the last expiration in the table, the extend toggle (see, The Extend Toggle, page 113) is turned on.

The Month Field

The month field displays the month and year of an option expiration. Clicking on the month field displays a matrix containing the Volatilities for the calls and puts in that expiration.

When the matrix appears, filtered values are displayed in light red. You will see filtered values only if the Filter toggle is on. If the Filter toggle is off (or if the Filter toggle is on and all the volatilities are within range), all values will be white.

You can also suppress a volatility by highlighting the volatility and pressing m. Deleting a volatility turns the volatility dark red and suppresses it from the input line. It is, however, still available. To un-delete a deleted volatility, click on it with the left mouse key. This changes its color to white and returns it to the skew.

Finally, you can also edit a particular volatility value. If you think a value is out of range but you do not want to delete it, you can edit it. To edit a volatility, double-click on it with the left mouse key. This opens an entry box. Type the volatility you want in the entry box and press b. This process creates a substitute volatility value. The substitute value is a locked value, and it will remain as you entered it until you unlock it. Unlocking the value causes the volatility to be recalculated and updated. This technique works for both filtered and un-filtered values.

In volatility chart windows, the input lines are affected by these actions. Filtered and deleted volatilities do not appear in input lines, and do not play a role in calculating the skew curve. Edited volatilities show as large dots in input lines and do play a role in calculating the skew curve.

The Calls Toggle

The Calls toggle controls whether calls participate in the skew. The default is on. Set to on, calls are included in the skew. Set to off, calls are excluded.

The Puts Toggle

The Puts toggle controls whether puts participate in the skew. The default is on. Set to on, puts are included in the skew. Set to off, puts are excluded.

The Rollover Toggle

If the rollover toggle is on, the skew will automatically shift to the next expiration series as the current options expire. For example, when the September option expires, the skew automatically shift to the October expiration. The Rollover toggle is responsive to the skews created using a wildcard. A wildcard specifies a specific relationship to the lead-month expiration, and the Rollover toggle enables you to make this relationship a part of the skew definition. However, you don't have to enter a wildcard to use the rollover toggle. You can create a rollover using any volatility skew definition by toggling Rollover to on.

The Extend Toggle

The extend toggle enables you to create a skew curve from currently-trading option expirations and automatically apply the skew curve to new, far-out option expirations as they begin to trade. For example, if the fifth-out-month options have not begun trading yet, you can create a skew based on the fourth-out-month options and apply it to the fifth-month options when they begin to trade using the extend toggle.

The Skew Name

The Name field contains the name of the volatility skew as it will be recorded in the database if you choose to save it. You can name a skew anything you want, but we recommend you use the default names because they adhere to a convention that provides information about how the skew is defined. Notice that changing the rollover and extend toggles changes the skew name. These fields in fact change the behavior of the skew that is, what the skew will do when you apply it. The naming conventions are designed to help you quickly identify skew behavior by looking at the skew name.

The nuances of skew definitions are particularly evident in the Skew List dialog box, a tool that enables you to apply a skew to an option chart or quote window. (For more information on the Skew List dialog box, please read Database Skews, page 121.) Let's take a closer look at the naming convention.

The following table shows how the naming convention works. Given the symbol US, the skew creates the default name VS_USU5 (wherein U would be the current expiration month code). Toggling rollover and extend on and off changes the name as follows.

Toggle	Result
Both Rollover and Extend off	VS_USU5
Rollover on	VS_US#
Extend on	VS_USU5#
Both Rollover and Extend on	VS_US##

The Second Section

The fields below the first section control information used to calculate the skew curve.

Field	Function
Skew Curve	Displays the Skew Curve menu
Calculate	Toggles spontaneous skew calculation on and off.
Filter	Toggles the use of a filter in calculating the skew.
Points	Displays the Skew Volatility Matrix, which enables you to edit the calculated volatility at each strike.
Base	Volatility Displays the Base Volatility menu
Shift	Specifies the number of units to shift the skew. Use negative numbers to shift left, positive numbers to shift right.
Strike	Displays the operative strike (as specified in the Base Volatility field). If you select Custom in the Base Volatility, this field specifies the price you want to use as the base strike. The default is the underlying price. If you leave the value at its default, the base will move with the market; if you edit this value, the base strike will remain fixed.

Selection	Function
Database Save	Saves the skew to your database under the name displayed in the Name field.
Up Arrow	Moves the skew upward on the Y Axis.
Down Arrow	Moves the skew downward on the Y Axis.
Left Arrow	Moves the skew left on the X Axis.
Right Arrow	Moves the skew right on the X Axis.
Small	Displays the Volatility Skew Parameters menu in small characters and changes this toggle to read Large.
Draw	Draws the skew in the volatility skew window, leaving the Volatility Skew Parameters menu on the screen.
Done	Draws the volatility skew and returns you to the active volatility skew window.

The Skew Curve Field

The Skew Curve field contains the selected skew curve type. Selecting the word in the Skew Curve field displays the Skew Curve menu, which contains all the available skew curve types. For all curve types except the Avg Implied, the software uses a least squares curve fitting technique to generate a polynomial (matching the formula listed below) that best fits the input volatility points. You can choose from the following skew curve types:

Selection	Calculation
Avg Implied	Average of implied volatilities on all input lines.
Linear
Quadratic
Cubic
4th Order
5th Order
Hyperbolic
Hyperbolic 3
Hyperbolic 4
Hyperbolic 5

Higher order polynomials provide greater accuracy, but they are more sensitive to erratic volatilities in the input lines. Lower order polynomials create smoother looking lines, but are less accurate. One difference between quadratic and hyperbolic calculations is that quadratic calculations form an increasingly sloped line as they approach infinity while hyperbolic calculations form a straight line as they approach infinity.

The Calculate Toggle

The calculate toggle turns skew calculation on and off. During the skew definition process (that is, when you display the Volatility Skew dialog box from the Vlty Skew menu), the calculate toggle is set to on. When it is on, the toggle displays an asterisk. By contrast, when you are editing or applying a skew, the calculate toggle is off.

The Filter Toggle

Toggles the use of a filter in calculating the skew. When turned on, erratic input points are automatically ignored during the skew curve calculation. You can identify filtered prices by displaying the matrix available through the Month field (see, The Month Field, page 112).

The Skew Volatility Matrix

Selecting the Points field displays the Skew Volatility matrix, which displays the calculated volatility at each strike:

In the left column, you see the strikes stated in their relationship to the at-the-money strike. For example, a negative 50 indicates a strike that is 50 points out-of-the-money.

In the right column, you see the volatility for the respective strike as calculated by the current skew. You can edit these volatility values by clicking on them. This displays an entry box which enables you to enter a different volatility. Changing a volatility renders the value in cyan (light blue), which means the value has been edited and locked. A locked value will not change. To unlock the value, click on it with the left mouse key.

The Skew Volatility menu contains a limited range of option strikes; however, other strikes are available. To see these strikes, use the e and r keys, or use the arrow selections at the bottom of the window. The following tables summarize the content of the Volatility Skew Matrix:

Field	Function
Strike	Displays strikes relative to the Base Volatility Value.
Skew	Displays the volatility of the respective strike calculated by the current skew.

Selection	Function
Draw	Draws the skew using the current values in the matrix.
Done	Draws the skew and returns you to the Volatility Skew Parameters menu.

The Points Field

The points field indicates the total number of points calculated in the skew curve. This number is a function of a) the range of the X Axis (strike prices), and b) the minimum difference between two adjacent strikes. You can change the number of points by selecting the number in this field and entering the number of points you want. Lowering the number of points makes it easier to define your own skew volatilities. Increasing the number of points increases the curve resolution.

The Base Volatility Menu

The Base Volatility field enables you to specify which option strikes you want to use to calculate the base volatility. You specify the strike you want by selecting the Base Volatility field and making a selection from the following menu:

Selection	Function
At-Money	Uses the at-the-money strikes as the volatility anchor.
At-Money+	Uses the closest in-the-money strikes as the volatility anchor.
At-Money-	Uses the closest out-of-the-money strikes as the volatility anchor.
At-Money+-	Uses the closest in-the-money and the closest out-of- the-money strikes as the volatility anchor.
Custom	Uses a volatility you specify as the anchor volatility; the skew curve moves only along the X axis with the price of the underlying instrument; the curve remains fixed along the Y axis.
Cancel	Returns you to the Volatility Skew Parameters menu.

The base volatility, or anchor volatility, is the average of all the implied volatilities of the options specified by the base volatility field and the curve definition. For example, if the skew definition uses calls and puts, two expiration chains, and the base is at-the-money, the base volatility is the average implied volatility of four options: the at-the-money put and call for both expirations.

The base volatility has significance during curve application. It is the point that moves the skew curve as the market's implied volatility changes. When you save a volatility skew, you are saving a curve shape and an anchor (base) point definition. When you apply a volatility skew, the base volatility is calculated, and the skew curve is anchored to it. If the base is the at-the-money strike and the volatility of the at-the-money strike increases, the entire curve rises on the Y axis; similarly, as the at-the-money strike changes (which implies a change in the underlying price), the entire skew curve follows it along the X axis.

During the definition process, the difference between the calculated base volatility and the skew curve volatility at the base strike price is shown in the Shift field. The value in this field indicates how well the curve matches the base, at the moment. The smaller the Shift, the closer the match. When the curve is applied, it is anchored to the base volatility, and the Shift will be zero (0).

Database Skews

Choosing Database Skews from the Vlty Skew menu displays the Volatility Skews menu. Here, the menu contains all defined volatility skews. To choose a skew, click on the skew you want to displays and select Done, or type a skew's name in the Skew Name field and press Enter.

Field	Function
Name	The name field lists the skew name as it has been saved to the database. Use the Skew Name field for quick lookup.
Date	The first option expiration for which this skew is defined.
CP	If the skew applies to both calls and puts, this field contains "CP". If the skew applies only to calls, the field contains a "C". If the skew applies only to puts, the field contains a "P".
R	If rollover is set to on, this field contains an "R".
Months	Lists options expirations (by month code) for which the skew is defined. If the extend toggle is set to on, ellipses follow the last month code.
Skew Name	Enables you to look up a volatility skew by typing a name and pressing Enter.

Selection	Function
Enable Delete	Toggles the menu in and out of delete mode.
Done	Displays the selected volatility skew.

Knowing how to read the Skew List dialog box is important. The Skew List dialog box is your tool for displaying and applying volatility skews, so knowing how to read a skew's definition using the fields in the Skew List dialog box saves a lot of time.

In the following skew definition,

VS_US#2# Sep05 CP R U Z H...

you see first the skew name, VS_US#2#. The name is followed by the date of the first options expiration chain defined by the skew. The third element in the definition tells you whether the skew has been defined to apply to calls, puts, or both using the codes C, P, and CP, respectively. The fourth element signals whether the skew has been defined to rollover; if it has, an R will appear in the field, and if it has not, the field will be empty. The fifth field is about sixteen characters wide so that multiple expiration month codes can be displayed; it indicates, using the common alpha codes for expiration months, the option expirations chosen for display in the skew. Finally, the sixth field indicates whether the skew definition is set for extension; if it set for extension, an ellipsis (...) is displayed following the last month code, and if it not set for extension, no ellipsis is displayed.

As you can see, you can tell quite a lot about a skew just by looking at its definition in the Skew List dialog box. This is important. Being able to read a definition in the Skew List equips you to make informed selections during the skew application process.