
Stochastic Log Volatility Market Model (C3 Phase III) (December, 2010)
Article Summary:
This article describes the sample AAA SLV Model made available in the attached dataset (version 12.6.99.003) and how to use it in generating stochastic scenarios. The dataset contains a Dynamic Scenario set, a Scenario Generator, and the sample AAA SLV Model which generates interest rate scenarios. The sample model is based on the attached AAA Economic Scenario Work Group report on the Stochastic Log Volatility interest rate scenario generator.
Background^{1}
Effective April 23, 2009, the Economic Scenario Work Group (ESWG) of the Life Financial Soundness/Risk Management Committee released a Stochastic Log Volatility (SLV) interest rate scenario generator model that can be used in interest rate modeling for life and annuity principlesbased capital and reserve calculations.
The SLV model developed by the ESWG "is consistent with the previous interest rate model approved by the NAIC during the C3 Phase I project" completed in 1999. This Academy SLV generator will adapt to "changing economic environments, allowing consistency from year to year in interest rate scenario selection". "The ESWG, along with the Academy’s Life Capital Adequacy Subcommittee, recommends that the SLV generator replace other interest rate generators currently in use for all regulatory purposes. To the extent a company is exposed to other financial market risks such as equity, credit and currency risks, these risks will also need to be modeled by the actuary, as well as any correlations between these risks. Note that the equity scenarios provided by the Academy for C3 Phase II RBC requirements continue to be appropriate."
The final "goal of the Academy is to develop an integrated debtequity generator that can be used for all reserve and capital calculations". Since the ESWG has not yet accomplished this goal, the sample AXIS User Defined Stochastic Generator should be modified based on updated parameters, and the latest recalibrated interest rate generator of the AAA’s C3 project. As such, the user should ensure that the Sample generator model attached with this document is appropriate for his/her purpose and is updated with the latest information on the AAA website if deemed necessary. For more details on this generator model, please also consult the AAA website whose link is provided at the bottom of this article.
Sample AAA SLV Model in AXIS (using AXIS 12.6.99.003)
The sample model is available in the attached dataset below. The sample AAA SLV Model is constructed using AXIS' User Defined Stochastic Market Model functionality. The User Defined Stochastic Market Model provides a flexible approach to modeling market variables such as interest rates, equity returns, inflation, etc. by means of AXIS script, which allows the user to program any model he/she wishes.
Prior to working with Scenario Generators and Scenario Sets in a dataset, you must activate the Market Model feature. You can find it as Feature # 76  Market Model in the list of "Features available for use" on the Custom Codes tab of the Dataset Parameters dialogue. You will require an activation code from GGY to unlock this feature.
To view the sample AAA SLV Model:
 Save and restore the attached dataset.
 Select User Defined Stochastic from the View/Global Scenario/Market Model Menu to display the list of User Defined Stochastic Model objects.
 In the AAA ESWG SLV model, five formula tables are available to parameterize and codify the model:
 Variable to index mapping: Table AAA ESWG SLV model vars map
 This table defines the names for parameters used in the remaining tables. It is recommended that this table should be Superprotected after it has been reviewed.
 Initialization: Table AAA ESWG SLV model PreProc1
 This table is used to enter initial data and parameters of the model.
 The initial US Treasury yield curve at 30th September 2008, the calibrated model parameters, and the correlation matrix are entered here.
 Preprocessing: Table AAA ESWG SLV model PreProc2
 Used to calculate the parameters of the model based on the data and calibrated parameters entered in the Initialization table. It can also be Superprotected.
 The historical yield curve data file required by the AAA model is specified in this table. The full path of this file must be entered in this table. Note: the sample refers to this file in c:\spare\AAA_historical_data_Sept2008.csv. To build scenarios using this historical data file, save this file (attached below) in your c:\spare directory.
 Cholesky decomposition of the correlation matrix (auxiliary function needed) and the mean reversion parameter take place in this table.
 Scenario generating: Table AAA ESWG SLV model ScnProcess
 Used to generate values in the scenario. The output can be stored in a 1200by29 table or directly in an AXIS Scenario.
 In the AAA SLV model the following simulations are performed in the Scenario generating table:
 Generate the correlated logarithm of the long maturity interest rates, the logarithm of the volatility of the longterm (20year) rate process and the nominal spread between the longterm and shortterm rates (auxiliary function needed).
 Derive the short (1year) and midterm (7year) rates.
 Complete the yield curve by adopting the pattern of the “best fit” historical curve, which produces the lowest weighted sum of squared deviations (auxiliary function needed).
 Postprocessing: Table AAA ESWG SLV model PostProc
 Used to adjust the values generated in the Scenario processing table and store the adjusted values in an AXIS scenario. For example, this table can be used to convert rates to the specified rate type in the scenario generator.
To generate interest rate scenarios using the sample AAA SLV Model:
 Select "AAA ESWG SLV model Scenario set" from the View/Global Scenario/Scenario Set Menu.
 To specify the desired scenario format, number of scenarios, curve and rate types, random number generator, seed etc., edit the "AAA ESWG SLV model generator" and make your selections in the wizard screens. Note that the random number generators available in AXIS may not be the same as the one used by the AAA Excel generator. As such the generated scenarios may not be identical to those generated using the AAA Excel model.
 Click the "Build and View" button to generate scenarios. Note: the sample refers to this file in c:\spare\AAA_historical_data_Sept2008.csv. To build scenarios using this historical data file, save this file (attached below) in your c:\spare directory.
For more information on the User Defined Stochastic Market Model, please refer to the following help page: https://ggy.com/htmlhelp/axis/45694.htm.
^{1} Sources: http://www.actuary.org/life/phase3.asp, and http://www.actuary.org/pdf/life/lbrc_dec08.pdf.
