Volatility Skew Structure

A Volatility Skew Structure is a World Variable which is used to specify a surface for the Price Volatility of a Security.

The surface is used to interpolate that volatility which should be used to price an option on the underlying security. This volatility can be interpolated using the desired Term of the option, Strike Price of the option and the Spot Price of the underlying security. Both the Strike Price and the Spot Price must be specified in the same currency. A Normalized Strike can then be computed from the Strike and Spot Prices by dividing the Strike Price by the Spot Price. This Normalized Strike along with the Term can then be used to interpolate the desired volatility.

Representing the surface in terms of a Normalized Strike is a very useful way of capturing the shape of the volatility surface which should be applied during Sensitivity Analysis of Portfolios. For example, consider a portfolio of options in a particular security. When testing the sensitivity of this portfolio's value against the spot price of the security, it is necessary that the same shape of volatility surface be used at each valuation scenario no matter what the spot price of the underlying is at that scenario. This ensures that all options on the underlying security in the portfolio will be valued using the best estimates of volatility for their respective strike prices under that scenario. A Volatility Skew Structure facilitates such analysis using the Normalized Strike representation for the volatility surface.

The first item that must be specified for a Volatility Skew Structure is whether the data for this volatility surface will be Date Specific or Term Specific. If the data will be date specific then select the "Term Dates Fixed" button; otherwise, for term specific data select the "Terms Constant" button. This item can be changed only if all existing volatility surface data has been deleted.

The next important specification is the Price Currency for all subsequent volatility data that will represent the volatility surface. This specification of this currency can only be changed if all existing volatility surface data has been deleted. [All internal requests for volatilities are correctly converted from this price currency into the desired price currency, provided that the data needed for conversion is made available via a Price Correlation Structure and other Volatility Skew Structures.]

The final specification impacts the display of the volatility surface. "Terms" specifies the number of points that will be interpolated over the time axis and "Years" specifies the length of this time axis in years. "Strikes" specifies the number of points that will be interpolated along the Normalized Strike axis which is specified by the two other values.

The following is a display of a Volatility Skew Structure on the EURO currency:

volskws1.gif

In order to see the graph of the volatility surface click on the "Chart" button to display:

volskws2.gif

To return to the main display, click on the "Restore" button.

In order to examine how the data has been set up, select one of the items in the list box with the Volatility Skew Structure Data. For example, selecting "EURO_VSS_3_MTHS_1.3" will display:

volskwsd.gif

This display shows the 3 month volatility on the EURO priced in USD for strike prices that are 130% of the spot EURO price in USD. This volatility is also specified as a Mid-Market volatility along with a Spread.

The current Mid-Market volatility is 6.0 % and the current volatility Spread between the bid and ask volatilities is zero.

The Mid-Market volatility formula shows that the current value is directly set to 0.06. And the Spread formula shows that the current value is directly set to 0.0.

Naming Convention:

The Volatility Skew Structure Data names are automatically created by first adding the term information to the end of the name chosen for the Volatility Skew Structure. The suffix that is added depends on whether the data is Date Specific or Term Specific. Once the term information is added then the Normalized Strike information is added to the end of the name.

Furthermore, the World Variable Data variables that are used to specify the Volatility Skew Structure Data are also named automatically. These names are generated using the generated name for the Volatility Skew Structure Data and then adding the appropriate suffix from the following list: