ESG Model Overview

The ESG selected by the NAIC will be used to produce a Basic Data Set of scenarios to be prescribed for statutory reporting. The Basic Data Set would include scenarios of Treasury Yields, Bond Returns and Equity Returns. The vendor has provided documentation as well as sets of scenarios on the NAIC website.

The following is an overview of each of the three component models in the ESG.

Treasury Interest Rate Model

The Treasury Interest Rate model is a standard finance Cox-Ingersoll-Ross 3-factor interest rate model with the following attributes:

1. Realistic yield distributions
2. Produces all commonly observed yield curve shapes, including inversions (e.g. historically, 10% of the time in the US)
3. No exploding yields
4. Fits the initial yield curve

The Treasury Model fits its three state variables to the 3-month maturity and 2 other selected points that are chosen each period to optimize the fit of the modeled interest rates to the initial Treasury yield curve. The modeled curve is then adjusted to fit the initial Treasury Yield curve using a deterministically generated shift function. The adjustments for fit are applied through the simulation period using an exponential "decay" parameter which controls the speed at which the adjustments decrease. The "real-world" default value of 3 for the decay parameter results in 95% reduction within the first 12 months. For risk-neutral, the decay is 0. The adjustment factors by tenor roll down the curve with the passage of time (e.g. the initial 10-year adjustment impacts the 8-year yield after 2 simulation years).

The drivers of the model produce parallel shifts, changes to slope and changes in curvature which affect the convexity of assets and liabilities. Potential yield curve shapes can include negative interest rates. According to documentation of the goals for the NAIC ESG, negative yield rates have occurred in the US in the past less than 0.4% of the time for the 3-month rate but never at the 5-year or 10-year maturities.

The range of results for long simulations avoids exploding yields through the speed and level of mean reversion parameters. The speed of mean reversion, level of mean reversion and interest rate volatility all contribute to simulating low rates for an extended period of time (since 2012 the 10-Year US Treasury has been approximately 2% on average). The mean reversion target (MRP) is determined using the same methodology as the AIRG model based on the following weighted average of observed rates:

The results of the Field Test (which the NAIC had planned for June to August 2021 but has subsequently postponed to 2022) will be used to refine some of the following parameters and decisions:

1. Decay Parameter
2. Negative Rates - how low, how frequent, and absolute floor
3. Mean reversion speed - long-end and short-end
4. Interest Volatility - long-end Yield (1 year volatility), short-end yield (1 year volatility), absolute minimum 3 month yield, achieved minimum 3 month yield (historically, long term interest rate volatility has been greater than short term interest rate volatility)
5. Arbitrage free - once a floor is added then the model is no longer arbitrage free
6. Calibration - which historic period captures appropriate market dynamics (e.g. 1953 vs 1995?)
7. Range of scenario high and low values
8. Persistency of low interest rate environments
9. Combinations of low short term rates (near zero) with significant volatility in long term rates - this is a significant flaw with the CIR model where long rates can't move if short rates don't move and the model can't capture long term volatility if the short rate doesn't move

Bond Fund Model

The Corporate Bond Fund model is still being refined but the goal is to have the following attributes:

1. Model individual bonds
2. Incorporate stochastic spreads, transitions (credit migration) and defaults
3. Capture issuer concentration risk
4. Produce jump-like behavior in spreads observed during the 2008 financial crisis
5. Market consistent fit to the initial spread curves
6. Imperfect correlations between spreads

Equity Return Model

The Equity Return model is a Stochastic Volatility with Jumps model with the following attributes:

1. Realistic return and volatility behavior
2. Jump process produces crisis-like events
3. Able to price derivatives, including volatility "smile"
4. Able to fit to market prices of options

The Equity Model provides returns for representative equity funds offered in US Life Insurance products. The returns are split between dividend income and price change which when combined gives the total return. The dividends modeled are linked to the 10-year Treasury yield and negatively correlated with S&P price movements. This linkage between the Treasury and Equity models is common in academic models, however, it has weak historic support and is not frequently observed in the real world.

Most equity models have stochastic volatility because this allows for fatter tails in the scenario distribution (e.g. facilitates big drops like 2008 financial crisis or Black Monday). The Equity Return model will have the ability to generate very large losses and gains in short periods of time (e.g. 2Q 2020) via a "Jump" process. The possibility of long recovery after a period of losses is driven by volatility and expected return. Generally, there is higher correlation in tails of equity scenarios.

The outstanding decisions with this model include:

1. The AIRG is calibrated with returns back to 1955, this calibration may be refined by regulators.
2. How frequently to update initial volatility (e.g. update with recent market movements)?
3. How to define targets that impact the "Jump" process by skewness and kurtosis?
4. Review correlation matrix, frequency of updates and specific historic period used in calibration.
5. Review link and relationship of equity returns and risk-free Treasury rates.