Volatility Surface Calculation

7.16 Volatility Surface Calculation

When you have defined a Forecast Rates and assigned the percentage shock amount to one or more rate scenarios, then the following formula is used for target ALM surface:

Target ALM Surface = (1+(SHOCK_AMT/100))*ALM_Vol

Where:

SHOCK_AMT is the specified value from FSI_FCAST_ALMVOL

ALM_Vol are all values from the target ALM Surface matrix (FSI_IRC_VOL_SURFACE_RATE_HIST)

Examples:

ALM Vol Surface Shock Calculations

For example, if there are no shocks applied, that is following base ALM vol surface with original values:

Table 7-32 Example of ALM Vol Surface Shock Calculations

Expiration Date
Strike	12/31/2010	6/30/2011	12/31/2011	6/30/2012	12/31/2012	6/30/2013
2	25	30	35	40	42	45
3	27	30	33	36	39	42
4	29	32	35	38	41	44
5	31	34	37	40	43	46
6	35	38	41	44	47	50

If you have specified a value of 1 as the percentage shock for Scenario One, then FSI_FCAST_ALMVOL. SHOCK_AMT = 1

In the subsequent forecast for Black 76 embedded option valuation, the Application will apply this percentage to all values in the matrix. For example, for Strike 2, the initial value was 25% (on 12/31/2010) and the up shock of 1% would be calculated as:

(1+(1/100))*25 = 25.25

This calculation is repeated for every remaining volatility entry, as shown:

After 1% Up Shock:

Table 7-33 Example of ALM Vol Surface Shock Calculation after 1% Up Shock

Expiration Date
Strike	12/31/2010	6/30/2011	12/31/2011	6/30/2012	12/31/2012	6/30/2013
2	25.25	30.3	35.35	40.4	42.42	45.45
3	27.27	30.3	33.33	36.36	39.39	42.42
4	29.29	32.32	35.35	38.38	41.41	44.44
5	31.31	34.34	37.37	40.4	43.43	46.46
6	35.35	38.38	41.41	44.44	47.47	50.5

The same procedure is repeated if the shock scenario were a negative amount, for example, -1% shock amount. The formula would be: (1+(-1/100))*25 = 25.25

Note:

The shock amounts are always applied to the Base scenario. This process is repeated for all remaining volatilities, as displayed.

After 1% DOWN Shock:

Table 7-34 Example of ALM Vol Surface Shock Calculation after 1% Down Shock

Expiration Date
Strike	12/31/2010	6/30/2011	12/31/2011	6/30/2012	12/31/2012	6/30/2013
2	24.75	29.7	34.65	39.6	41.58	44.55
3	26.73	29.7	32.67	35.64	38.61	41.58
4	28.71	31.68	34.65	37.62	40.59	43.56
5	30.69	33.66	36.63	39.6	42.57	45.54
6	34.65	37.62	40.59	43.56	46.53	49.5

The ALM Volatilities are stored is FSI_IRC_VOL_SURFACE_RATE_HIST. When a user defines an ALM Shock, it is joined to this table by INTEREST_RATE_CD. An ALM Vol Surface can have multiple effective dates but this is irrelevant until processing occurs as only one As-of Date is selected in a process:

INTEREST_RATE_CD: defines the ALM Vol surface unique code
EFFECTIVE_DATE: The effective date of the ALM Vol. This should match the As-of Date in a process.
EXPIRAITON_DATE: Nominal date dimension for ALM Vol (horizontal)
VOL_SURFACE_STRIKE: The nominal strike value dimension (vertical)
VOLATILITY: Numerical volatility percent (that is 40 is interpreted as 40%). This is the amount that is shocked when users define a shocking percentage in FSI_FCAST_ALMVOL. SHOCK_AMT. This new shocking amount is the new volatility that is applied in Black 76 option value calculations for every scenario in the forecast.

Example:

If there is a qualified existing ALM Vol Surface defined in FSI_IRC_VOL_SURFACE_RATE_HIST, as follows:

Table 7-35 Details of FSI_IRC_VOL_SURFACE_RATE_HIST table

INTEREST_RATE_CD	EFFECTIVE_DATE	VOL_SURFACE_STRIKE	EXPIRAITON_DATE	VOLATILITY
USD Vols	12/31/2010	5	6/30/2011	10
USD Vols	12/31/2010	5	12/31/2011	20
USD Vols	12/31/2010	5	6/30/2012	30

The table FSI_FCAST_ALMVOL is populated as follows:

Table 7-36 Details of FSI_FCAST_ALMVOL table

OPTION_VOL_IRC_CD	SCENARIO_NUM	SHOCK_AMT
USD Vols	A	1%
USD Vols	B	-1%
USD Vols	C	3%

Thus, in a forecast for Scenario A, all ALM vols would receive a 1% shock using the definition above. This is repeated for every scenario (A, B, and C) in the FCR definition for the Process Forecast.