New Features In The OAD Analyzer (January, 2013)
The OAD Analyzer batch in AXIS has new flexible functionality giving you a very powerful risk management tool within AXIS. The batch can now be used to calculate an Option-Adjusted Spread to calibrate the present value of asset cashflows to their inforce or calculated market values. This OAS can then be used in discounting on the asset and liability side to produce Market-Consistent Option-Adjusted Duration and Convexities for a segment of assets and liabilities. These durations and convexity will be calculated in aggregate. The user-defined partial duration bands have been extended to support up to 12 bands that can extend out to 50 years. This partial rate duration feature in this batch has become a very useful tool for illustrating the granular duration & convexity profile of your assets and liabilities, as well as a powerful risk management tool for monitoring the gaps between them.
Sounds Great But How Does The Process Actually Work?
First, AXIS will generate as many scenarios as you specify using the Calibrated correlated Monte Carlo Simulation Model (help text). The simulation of this set of scenarios will be calibrated to match the zero-coupon bond prices implied by the base scenario (). The base scenario can be the yield curve from the historic scenario, future scenario, or just a yield curve defined by the user in the batch dialogue screen.
These calibrated scenarios will be used to project cashflows for the assets and liabilities. These scenarios represent different interest rate paths of which some may trigger optionality embedded in the assets/liabilities. For example, imagine a liability in which the lapse rate increases as interest rates rise. In some of these generated scenarios, interest rates rise, increasing lapse rates in the liability projections, while in other scenarios they don’t. Because the scenarios are calibrated to the Base scenario in aggregate, AXIS is calculating an unbiased estimate of the option-adjusted cashflows for the liability where the option is the lapse rate.
The scenarios will also be used to discount these cashflows back to time zero using the 90-day rate at each month for discounting. Summing these discounted cashflows across a single scenario will produce an aggregate PV for that scenario. Averaging the PV’s for all scenarios will give the PVMidAssets, PVMidLiabilities, and PVMidNet referenced in the help text for the OAD Analyzer.
What About The OAS Calculation?
The batch can now be used to calculate an Option-Adjusted Spread to calibrate the total present value of asset cashflows to their inforce or calculated market values at the valuation date. AXIS accomplishes this calibration by calculating an additional spread that is added to the 90-day rates of all scenarios used for discounting. Because these different interest rate paths take into account embedded optionality in the cashflows, this spread is referred to as the Option-Adjusted Spread. The OAS is limited to a range from -50% to 100%. This is a valuable metric to have as a risk management tool on the investment side.
The user now has the option to incorporate the OAS (or any scalar spread of their choosing) into the discounting on the cashflows to generate the PVMidAssets, PVMidLiabilities, and PVMidNet. This means present values on the asset and liability side will be calculated using the same discount rates, allowing the user to compare apples to apples when viewing asset and liability present values, durations, and convexities.
How Are the Durations and Convexities Determined?
In order to calculate the durations, the base yield curve will be shocked up and/or down by 12 times the shock amount specified on the “Duration Calculations” tab of the Dataset Parameters. Yield curves will be randomly generated and then calibrated based on these shocked Base yield curves. These calibrated curves will be used in the same methodology described above to produce PVUp and PVDown amounts for assets/liabilities/net. With these amounts, durations and convexities are calculated by AXIS (detailed formulas are contained in the help text for the OAD Analyzer).
What About The Duration Bands?
The user can specify duration bands to be consistent with the duration bands table on the “Duration Calculations” tab of the Dataset Parameters. In this table, the user can specify up to 10 duration bands that extend out to 30 years (help text). There is also an extended partial duration table in which the user can specify up to 12 duration bands that extend as far as 50 years out (help text). To use the extended table, the user will need to select it specifically in the dialogue screen when creating the OAD Analyzer batch. The shock can be a flat shock along the duration band or an interpolated shock. The shock can be applied to forward rates or spot rates. Note that for each band, AXIS will need to create two extra Base shocked scenarios for the up and down shocks. So if you want to generate 5 scenarios, and calculate partial durations on 10 different bands, there are 10 x 5 extra scenarios that need to be generated for each of the up and down shocks, resulting in 100 extra scenarios to be generated. Because of this large increase in scenario generation, the use of duration bands can significantly increase the runtime of the batch.
I Want To Use My Own Scenarios Instead Of AXIS Generated Scenarios - Is That Possible?
Of course it is! In step 4 of the OAD wizard you can tell AXIS that scenarios should be imported. You will need to specify 3 scenario sets: un-shocked scenarios, shocked-up scenarios, shocked-down scenarios. In step 5 you will need to tell AXIS the amount that the yield curve is shocked for the up and down scenarios, as well as the band of the yield curve that the shock applies to. The scenario sets you provide will be used for the cashflow projections and discounting, as well as calculating the OAS, Duration, and Convexity.
What Will The Output From This Batch Look Like?
The batch will output 2 tables to the Import/Export Database. The Detailed result table will display the average PV of cashflows for each set of scenarios (Level, Shocked-Up, and Shocked-Down) for each duration band. If you have chosen to not calculate partial durations, then only 1 band will be shown which encompasses the entire yield curve. The Summary table will show the resulting spreads, durations, and convexities for the assets, liabilities, and assets net of liabilities.
Table 1 – Partial Duration Band Example:
Table 2 – Partial Duration Band Example: