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2005 Seg Fund Guarantee Capital Model (March, 2009)

Article Summary:

This article describes the “2005 Seg Fund Guarantee Capital Model” (hereon referred to as “the Model”) and how to use AXIS Script functions to create a User Defined Stochastic Generator in AXIS (version 12.5.99.008 in Fixed Scenario Format and version 2013.09.01 in Flexible Scenario Format). A sample AXIS Dataset containing the Model is attached.


Background

The “2005 SEG FUND GUARANTEE CAPITAL MODEL” is a User Defined Stochastic Model, which may be used for reserving and capital calculations. This model is an integrated model that reflects the relationship between yield curve and equity.

The calibrated parameters in this model are based on the attached document and are for demonstration only. The parameters should be reviewed and updated if necessary.

A sample AXIS Dataset (2005 SEG FUND GUARANTEE CAPITAL MODEL.ZIP) illustrating the modeling technique and the corresponding model description document (2005 Prescribed Factors for SFGC.pdf) are attached at the bottom of this article.

Summary of Process (in AXIS Version 12.5.99.008 in Fixed Scenario Format) & (in AXIS Version 2013.09.01 in Flexible Scenario Format)

In order to use the Model for generating scenarios, it must be used within a Scenario Generator, which in turn must be used within a Scenario Set. A Scenario Generator is an object that allows you to create and save an algorithmic definition of a deterministic or stochastic set of scenarios. The Market Model is referenced from the Scenario Generator, and defines the characteristics of the stochastic Scenario Set to be created.

This process requires that the following four steps be executed in the order listed:

  1. Create a new Market Model.
  2. Create a new Scenario Generator object that references the new Market Model.
  3. Create a new Dynamic Scenario Set based on this Scenario Generator.
  4. Build the Future Scenarios using this Dynamic Scenario Set. As an option, save them as a Static Scenario Set.

This document will mainly focus on the first step: How to create a new Market Model. For steps 2, 3, and 4, please refer to AXIS Online Help.

Create the Model Scenario Generator (in AXIS Version 12.5.99.008 in Fixed Scenario Format) & (in AXIS Version 2013.09.01 in Flexible Scenario Format)

Prior to working with Scenario Generators and Scenario Sets in a dataset, you must first 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 must obtain the activation code from GGY to unlock this feature. The User Defined Stochastic Market Model provides a flexible way to model market variables such as interest rates, equity returns and inflation. This can be achieved by using AXIS script, as follows:
  1. Select User Defined Stochastic from the View/Global Scenario/Market Model Menu to display the list of User Defined Stochastic Market Model objects.
  2. Create a User Defined Stochastic Model object. You can either create it based on the Vendor Defaults setting or an Existing User Defined Stochastic Model. The New User Defined Stochastic Model wizard prompts you to select an existing formula table or create a new one for each of the five Model Description modules.

Details on the five tables are,

(1)   Variable to index mapping table

It should be used to define names for parameters used in the remaining tables. It is recommended that this table should be Superprotected after it has been reviewed.

(2)   Initialization table

It should be used to enter initial data and parameters of the model.

The 150 by 100 Numeric Grid in the Formula Tables may be used to input data.

(3)   Preprocessing table

It should be used to calculate the parameters of the model based on the data entered in the Initialization table. It can also be Superprotected.

Note that in Tables (2) and (3), results can be stored in three special Intertable arrays: Doubles, Longs and Booleans. Each Intertable array can store up to 10000 results, which can be shared in the remaining tables (4) and (5).

For the Model example, the following calculations are performed in the Preprocessing table:

  • Load up the correlation matrix

  • Apply Cholesky Decomposition to the correlation matrix (auxiliary function needed)

(4)   Scenario generating table

It should be used to generate values in the scenario. The output can be stored in a 1200-by-29 table or directly in an AXIS Scenario.

For the Model example, the following simulations are performed in the Scenario generating table:

  • Generate 9 correlated random Normal variables for the 9 different risk classes;

  • Simulate the long-term (10-year Government of Canada (“GOC”) Treasury Yields) and short-term (3-month GOC T-Bills) interest rates;

  • Derive the mid-term (5-year GOC Treasury Yields) based on the simulated long-term and short-term rates;

  • Complete the yield curve by assuming a linear relationship between the short-term to mid-term period, and mid-term to long-term period; after the 10th year, interest rates are assumed to be flattened out;

  • The low-volatility, diversified, intermediate and aggressive equities are generated based on a Regime-Switching-LogNormal (RSLN) model.

(5)  Postprocessing table

It should be 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.

For the Model example, it is assumed that:

  • The simulated yield curves for the money market and fixed income are in annual effective format.

  • The simulated growth rates for the diversified, aggressive, intermediate and low volatility markets are in annual continuous format.

Please note that when the results are written to the AXIS scenario, proper rate type and curve type need to be converted.

For more information on the User Defined Stochastic Market Model, please refer to the following help page: https://ggy.com/htmlhelp/axis/45694.htm.

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