Volatility

A measure of the extent to which a price parameter varies over a given period of time. The volatility, therefore, describes the positive and negative deviation of market parameters from their expected value. You use it to valuate transactions with optional components.

Once they have been calculated, a distinction is made between the following kinds of volatility:

• Historical Volatility

  Historical volatility is calculated on the basis of the historical data of the respective price parameter. Here the volatility is estimated on the basis of the standard deviation of the sample.

• Implied Volatility

  Implied volatility results from the option prices listed on the market for an underlying that represents the price parameter (for example, the value of a currency option for calculating the volatility of a currency exchange rate). The implied volatility reflects the expectations of the market for the future.

  Implied volatility is not the same for every term of the option. In the same way as for the yield curve, it is more the case that there is a volatility structure. Furthermore, where the terms are the same, the implied volatility depends upon the exercise price. This is the smile effect. For interest rate options or interest rate instruments, implied volatility also depends on the residual maturity of the underlying.

Within the market database, SAP gives you the option of saving (not calculating) implied and historical volatility. The system differentiates between historical and implied volatility by means of volatility categories. Here, you need to create different volatility types with different volatility categories in Customizing under  Cross-Application Components  Market Data  Volatilities  Edit Volatility Types .

• For historical volatility types, you can define exactly one value (in percent) for each date.

• For implied volatility types, you define the volatility structure for each date. You do this by specifying the degree of volatility as a percentage based on the residual maturity of the option, moneyness as a parameter for the dependency on the strike price, and the residual maturity of the underlying.

The system interprets the saved volatility as annualized volatility (that is, volatility with an assumed holding period of one year) in percent.

You can select the underlying of a volatility from one of the following:

• Currency pair (exchange rate volatility)

• Financial instrument or financial transaction (security volatility)

• Reference interest rate (interest rate volatility)

In addition, you can define volatility that is not based on an underlying in the system. In Customizing for Market Data under  Volatilities  Create Non-Underlying-Based Volatility Structures , define a volatility ID. This substitutes entering the underlying when editing volatilities.

The SAP system uses volatility to valuate optional products in the price calculator. The system behaves as follows:

1. The market data set is derived before the price calculator is called

2. The price calculator uses the market data set to determine the volatility ID of a volatility structure that is not based on an underlying or the underlying and transfers this to the interface used to read volatility.

3. The volatility structure is read by means of the underlying or the volatility ID

4. The appropriate volatility for the given parameters is determined using the Method for Calculating Volatility (neighbor search or interpolation)