Market Consistent Valuation of Fixed Indexed Annuity
By Jing Fritz
Risk Management, February 2022
For the December newsletter, as we already have a Fixed Indexed Annuity (FIA) PBR paper in the pipeline, I volunteered to write an FIA article to supplement the FIA PBR paper for an FIA themed edition. My original thought was to talk about LDTI and IFRS 17, to complete the full circle of accounting and regulation changes in insurance, and their implication for FIA. As I started drafting the paper, I realized it probably adds more value to talk about the market consistent measurement and modeling of FIA contracts, so as to raise awareness of the importance of the market consistent valuation framework in internal management reporting of FIA, such as risk management and pricing.
General FIA Valuation
The valuation of an insurance contract starts at the product development and pricing stage. The pricing metrics an insurance company uses to gauge the profitability of their products could vary. One common practice in the US is to look at the after-tax distributable earnings (DE). It is from the perspective of the capital providers (i.e., shareholders and debt holders of the insurer). The stream of the projected DE, which is after retaining enough capital to maintain the target Risk Based Capital (RBC) ratio, is measured against the initial capital strain to test the profitability of the product. The spread of the internal rate of return over the cost of capital (e.g., Weighted Average Cost of Capital) could be one pricing metric. Instead of a percentage spread figure, management will also be interested to see the dollar amount value of the new business, which can be calculated as the differential between the present value of the DE, with the cost of capital as the discount rate, and the initial capital strain. This DE method can be used in the pricing of both businesses issued to policyholders and business acquired/assumed from another insurer.
One less common pricing practice is to look at the market consistent value (MCV) of the new business. For a traditional deferred annuity product, the MCV concept in pricing might be irrelevant unless a fair price needs to be calculated for a purchased block of business or the case of a company adopting MCV framework for management reporting. As a comparison, the writers of FIA, which by design applies equity indexed credits to the Account Value (AV) and to which Guaranteed Minimum Benefit (GMxB) riders could be attached, are more familiar with the concept of MCV as both equity-indexed credits and GMxB are forms of embedded derivatives.[1]
The real world (RW) distributable earning approach and the risk neutral (RN, i.e., market consistent value) approach are not mutually exclusive, rather they supplement each other as they each provide insights into the profitability or the value of an insurance product from different perspectives. The DE method provides the capital providers a view into the stream of distributable returns expected on their investment for the products. The assumptions behind the DE method though have the caveat of being quite arbitrary and could be subject to management bias. The MCV on the other hand is built on the principle of no arbitrage. It can produce the embedded value of the business as a present value of all future earnings, with market consistent assumptions, which is especially valuable for businesses with embedded derivatives such as FIA. The MCV calculates the fair price (e.g., fees in the context of FIA) to charge policyholders, connects the pricing with asset liability management (ALM) and hedging from the initial stage of the product cycle, and most importantly enables the full risk and return attribution analysis: All the risks in the complex product design is fully understood and adequately priced before the product is launched.
Trend Toward MCV
While the management reporting frameworks, such as pricing framework, are internally driven, the insurance accounting changes such as IFRS 17 and LDTI add momentum for insurers to adopt MCV framework for reporting purposes and to integrate this framework into other functionality such as pricing.
Pre LDTI, the excess benefit reserves for FIA follows SOP 03-1 and not all FIA writers use risk neutral scenarios in the calculation. For embedded derivatives under FAS 133, insurers might use deterministic option budgets to project the index credits so risk neutral projection is not needed. LDTI introduces a new concept called market risk benefit (MRB) which needs to be fair valued. The FIA GMxBs, falling under SOP 03-1 pre LDTI, will be MRBs post LDTI, thus are likely valued with market consistent assumptions. This also offers an opportunity for the modeling of the excess benefit liability to be aligned with that of the embedded derivatives (under LDTI, all future embedded derivatives for FIA will continue to be separated from the host from day 1) in that both can leverage the same set of market consistent projections.
Like Solvency II, the valuation principle of IFRS 17 is MCV. Different from LDTI, IFRS 17 deems the underwriting risks and financial risks of FIA too intertwined to be separated, so there is no separation between host and embedded derivative like LDTI. The total liability of IFRS 17 is made of three components: Best estimate liability (BEL), risk adjustment (RA), and contractual service margin (CSM). The RA is an explicit prudence provision for unhedgeable risks. The CSM at inception is basically the PV of profits that will be released into earnings gradually as the insurance service is provided. The concept of CSM can be well adapted in the realm of pricing to gauge the profitability of an insurance product. Beyond this point, BEL is used to reference liability calculated with best estimate assumptions, in the general sense, not in the context of IFRS 17.
Market Consistent Valuation
1. MCV General Guidance
For the companies that are interested in adopting an MCV framework, the first question that comes to their mind is probably where they should start. There are accounting standards providing guiding principles for fair value measurement. By no means the internal valuation or risk management framework needs to follow these standards, however, these standards lay the foundation of the MCV framework, and the pricing or risk management actuaries can make discretionary changes wherever they see fit.
While they don’t specify under what circumstances fair value measurement is required or permitted to be performed, both FAS 157 and IFRS 13 put forth a consistent framework for measuring fair value, regardless of the type of the asset or liability to be valued. The inputs used to measure fair value are categorized into three different levels. The fitness of each level of inputs to the fair value measurement for insurance contracts are discussed below:
Level 1: Market observable price
Level 1 is truly marked to market. Examples include the price of a traded stock. This requires that there is a deep and liquid market for the asset or liability. This requirement is not met for insurance contracts.Level 2: No active market—quoted price or modeled value with market observable inputs
While there are plenty of reinsurance transactions and insurance M&A activities, a quoted price probably is not available. Instead, insurers will have to rely on modeling to calculate the fair value of the insurance products. The discounted cash flow approach is typically the go-to modeling technique. Some of the inputs needed for the modeling, such as interest rates, could be observed from the market so they are under Level 2.Level 3: Last resort—modeled value with unobservable inputs
This is the least marked-to-market level. A few inputs can’t be observed from the market so the valuation will need Level 3 inputs from the fair value hierarchy.
Just like the complex investment contracts such as mortgage-backed securities, the fair value measurement of an FIA contract leverages a combination of quantitative models, market observable inputs and subjective assumptions.
The fair value accounting standards also require the fair value to consider the non-performance risks, including credit risk. However, incorporation of non-performance risks in the modeling for internal purposes is not really a requirement. Such inclusion in pricing will probably distort the estimation of the insurer’s obligation, producing contractual fees insufficient to support the policyholder benefits. For pricing purposes, it is generally accepted not to include non-performance risks.
2. Modeling Approach
The discounted cash flow (DCF) approach is the general approach used in fair value measurement of FIA. How they are applied for IFRS 17 and LDTI vary. The modeling for internal management purposes is not restricted by the accounting standards.
On a high level, a stream of cash inflows and outflows are projected until the business runs off. Initial premium (cash inflow) sets up the AV. The index credits, which are not cash flows per se, and additional deposits (cash inflow) grow the AV. Partial withdrawals (cash outflow), surrender charge (cash inflow), fees (cash inflow), etc., reduces the AV. After the AV is depleted, the excess benefits (cash inflow) will continue in the projection, for products with GMxB riders. These cash flows are then discounted to get the probability weighted prevent value.
3. Inputs, assumptions and methodology
As mentioned above, fair value measurement of FIA requires modeling with different inputs and how the value of the inputs is sourced varies by the type of assumptions.
In general, the financial inputs, such as interest rates, can be observed from the capital market. However, there is a limit to what can be observed from the capital model. One typical challenge is that the insurance liability tends to be much longer than the tenor of the corresponding capital market instruments. For instance, currently the US Treasury doesn’t go beyond 30 years in maturity; except for rare cases, the terms of the publicly traded corporate credits in the US are even shorter, as the market participants, probably other than insurers or pension funds, don’t have an appetite for long-dated corporate credits. The same can be said about the derivative market. Sometimes there are simply no traded instruments, with which the embedded derivatives can be directly replicated, and to which the market-consistent financial assumptions thereof can be calibrated.
The underwriting assumptions, however, are not observable and they are instead estimated by each insurer, combining the historical experience of their policyholders with actuarial judgment about future expectations. Mortality/longevity risk probably is the only underwriting risk that arguably could be observed, from academic research or underwriting manuals from large life reinsurers. The assumptions around policyholder behaviors, such as lapse and withdrawal, and their interaction with economic assumptions are more arbitrary and more company specific. That being said, there are vendors providing information service on insurance policyholder behaviors, albeit they are not as widely used as their counterparts in the capital market data space, such as Bloomberg and IHS Markit.
3.1 Financial Inputs and its Modeling
Interest Rate
What Interest Rate Should be Used?
While it is generally believed that the interest rate represents the time value of money in theory, which market observable interest rate to use is debatable. For instance, practitioners in banking will benchmark to different sets of interest rates than those in the insurance industry. The interest rates for an insurer, in the US, typically fall under two categories: US Treasury rate and LIBOR rate (or swap rate). The former is more applicable for general account asset backed insurance products (e.g., pension risk transfer) as US Treasury rates are the typical interest rate referenced for cash assets, such as corporate bonds. For instance, the credit spreads of a corporate bond are typically quoted as an excess rate over US Treasury. In practice, the LIBOR rate is the discount rate used by market participants in the risk neutral valuation/pricing of the derivatives in a liquid and deep market and includes a premium covering credit risks of the borrowing banks. LIBOR itself has a lot of flaws and soon will be replaced by so-called “risk-free rates.” The US dollar version of this “risk-free rate” is called SOFR (Secured Overnight Financing Rate). Theoretically the LIBOR rates should be higher than the US Treasury rates as there is an additional risk premium for interbank lending, however we’ve seen phenomenon that US Treasury rates are pushed up above the LIBOR rate of the same tenor at a few tenors due to various reasons, including Fed Reserve’s balance sheet management activity.
FIA or other equity linked products are unique because the index credit is funded by the portfolio yield of the general account assets, which determines the option budget. The treasury rate is the natural choice for the interest rate in the projection of portfolio yield. The portfolio yield also has a spread component that will be discussed in a later section. In comparison, the interest rate used in the discounting in the valuation of the embedded derivatives are more ambiguous. Accounting literatures don’t specify what interest rate to use. The actual practice could vary by insurer, insurance product, etc. For example, some insurers have used a hybrid rate combining both LIBOR rate (possibly subtracting a risk premium) and UST rate as the interest rate, on which an illiquid premium could be added (if the bottom-up approach is chosen), while others simply use one of the two, in discounting cash flows in the liability valuation for IFRS 17. Many insurers simply use LIBOR rate or swap rate as the interest rate in the fair value measurement (e.g., FAS 133, MRB) under US GAAP.
Deterministic Versus Stochastic Interest Rates
The interest rate and the spread are not necessarily separated in the projection of the portfolio yield that drives the option budget. If they are, the interest rate used is typically the Treasury rate. Real world scenarios can be used to forecast the future Treasury rates. AAA’s RW interest rate generator is one option. However, as the option budget will be used to solve for the values of the FIA product parameters such as cap rate and participation rate to ensure the option budget is met, stochastic on stochastic simulation is needed. The easier route might be to use a deterministic interest rate path for the option budget, which also simplifies the assumption setting of the spread in the option budget.
Having LIBOR rate or swap rate as the interest rate in discounting has its advantage in risk neutral or market consistent valuation in that derivatives in the capital market use LIBOR. Therefore, a variety of LIBOR market models, which are used to generate the risk neutral interest rate scenarios, are readily available. One common one is LIBOR market model (LMM) with SABR style stochastic volatility. The LIBOR models are usually calibrated to swaptions, traded in the market.
Since FIA typically has hedging in place to ensure index credit is fully or closely matched with the payoffs of the hedging instruments, LIBOR (or the replacement thereof) is supposed to be the discounting rate to ensure the expected index credits on average equals to the option budget. For pricing purposes, LIBOR rate is probably the preferred interest rate in discounting as well, to ensure a fair price is paid for the hedging and a fair price is charged from the policyholder.
In the case that a rate other than the LIBOR rate is chosen as the interest rate in discounting and a set of stochastic RN interest rates are needed, one option is to assume the differentials between the chosen rate and the LIBOR is deterministic and the differentials will be added after the LIBOR rate is calibrated using LMM.
Illiquidity Risk, Credit Risk, etc.
FIA insurers by and large take investment risks, probably except for the mismatch risk, in their invested assets to enhance the investment yields, in order to support the benefits afforded to the policyholders. For FIA, the investment risk spread as part of the portfolio yield will be projected to generate a future option budget, which in turn determines the index credits. The simplest approach will be to use a deterministic path, as it was discussed in the interest rate section. While the valuation of insurance contracts might need to be done on a seriatim level, the asset portfolio is managed on a more aggregated level, with the actual granularity varying depending on the ALM effort of each company. The index credits will affect future CFs in the valuation of the contract.
However, it is debatable whether the yield spread, in compensation of the investment risk, can be incorporated into the valuation of the insurance contracts, backed by these same investments. Specifically, can the discount rate of the cash flows be increased when the asset yields are higher? One argument against such a practice is that it gives insurance companies the incentives to take investment risks for the sole purpose of lowering the liability value. From an accounting perspective, it also means two companies would have a different measurement for an identical liability. Accounting standards typically don't permit the extra yield from the assets to be directly translated into an increase in discount rates.
In IFRS 17, an illiquidity premium (ILP), theoretically a compensation for the lack of liquidity in the insurance product, can be added on top of interest rate in discounting the fulfillment cash flows. The credit losses, which could be pegged to expected credit losses (ECL) under IFRS 9, were removed from the ILP. However, cash flows from both the insurance contract and the investments backing the insurance liability must be predictable for the illiquidity premium to be justifiable. The FIA cash flows are usually not predictable.
For internal modeling, it is probably a good practice not to add spreads to the interest rate for discounting.
Equity
Different from the direct participating insurance contracts such as variable annuity, the policyholder’s fund for FIA is not invested in the underlying index funds; instead, the crediting rate to the indexed account of FIA is linked to the performance of the equity market, the point-to-point price change of the equity index or indexes, to be precise. The price change of the linked index is further adjusted based on formulas including participating rates, caps and floors, etc. The reference index could be a major equity index such as SPX or, less commonly, a combination of different indices. A synthetic index could render the modeling of the embedded derivative quite challenging.
As mentioned already in the interest rate discussion, the index credits are supported by a portion of the portfolio yield from the general account assets, namely the option budget. Insurers mainly adjust the parameters such as caps, floors and participating rates to ensure that the PV of index credits in the risk neutral world will not exceed option budget. In the projection, these parameters can be adjusted, however, the projection needs to align with the reality that some of the parameters have a certain level of stickiness to it. If the parameters are moved out of sync from the peers, disintermediation risk will arise as policyholders have the option to surrender the policy and get more favorable returns elsewhere, especially after the surrender charge period has expired.
Black-Scholes (BS) options pricing model has been historically used to solve the future caps or participating rates for FIA. It has the advantage of being a closed form solution. However, BS has several limitations in its assumptions: E.g., constant risk-free rate and flat equity volatility. Since the introduction of BS, there have been a few models that have extended the BS. The Heston model is one example that adds in stochastic equity volatility. Furthermore, equity-interest rate hybrid models, such as a combination of Heston for equity and stochastic volatility extension of LMM for interest rate, allow for both stochastic interest rate and stochastic equity. No matter which model is chosen, the dividends need to be removed in the option pricing as FIA are really derivatives on the price turn.
The calibration of future caps, etc., are performed before the CF projections and PV of CFs are modeled in the actuarial model. Once the parameters, e.g., caps, are set for each of the future crediting segments, they will then be used in calculating the scenario path specific equity index credits for each contract, in the projection of AV, cash flows and so on, inclusive of all inputs and assumptions for modeling. For each of the scenarios, one stream of RN equity returns is paired with one stream of RN interest rates, just like how they are forecasted as part of the derivation process for product parameters.
3.2 Underwriting Inputs and its Modeling
Unlike financial risks, underwriting risks inherent within insurance contracts are not hedgeable. As a result, additional prudence is required to cover the potential adverse deviation in the underwriting assumptions. On top of the best estimate (BE) assumptions, a risk margin (RM) is needed for the underwriting assumptions. RM has its own special meaning and application within Solvency II (SII); however, it hereinafter represents the provision for adverse deviation (PAD) in the general sense.
A few approaches have been used in the quantification of the RM by insurers, including cost of capital (CoC) approach, value at risk (VaR) or tail value at risk (TVaR) measure, and discount rate haircut as a proxy. CoC was made popular by SII. It discounts the costs on future risk capitals for underwriting risks and is more computationally expensive than VaR or TVaR measure. VaR or TVaR are simpler, and they are the more popular choice for IFRS 17 as insurers are required to disclose the confidence interval for the RA or the equivalent confidence interval if a non-VaR measure is used for RA. RM as a discount rate haircut is a shortcut but nevertheless has been an acceptable approach. The discount rate haircut is solved so that the difference between the liability calculated with the inclusion of such a haircut and that without the haircut is exactly the RM amount, produced by the first principle calculation. The discount rate haircut has the advantage of easy implementation in modeling.
Financial engineering has advanced the modeling of financial inputs. However, the application of statistical analysis in forecasting underwriting assumptions haven’t had the same level of sophistication. Normal distribution is probably the most widely used distribution for underwriting risk variables, partly due to the central limit theorem. The t-distribution is also a candidate. The largest hurdle for applying the statistical techniques has been the lack of quality data. Lack of credible history is one major concern, especially when a brand-new product is launched. Even for products that have been in force for a few years, the focal point of the experience study has been on monitoring actual/expected (A/E) ratio and accordingly adjusting expected assumptions either in forecast of existing products or pricing of the new products to ensure future A/E ratio is close to 100 percent. Insurers were not required to explicitly separate BE and RM in reporting unless they were governed by SII. The need to enhance the experience study has become more imminent due to insurance accounting changes. LDTI requires the use of BE and the explicit tracking of actual versus expected for products under the old FAS 60. More relevant to FIA, the RM in the fair value measurement of VED and that for MRB need to be quantified. LDTI requires more detailed disclosure of experience results as well. Similar to SII, IFRS 17 also requires transparency of BE and RM.
For now, insurers leverage both quantitative method and actuarial judgement, in determining BE and RM. While the practice could vary, generally speaking the assumption setting follows these steps:
- Each underwriting assumption is analyzed independently. Even for the same type of assumption, there could be further breakdowns by product type, demographics of policyholder and so on. The BE are typically in a tabular form. A/E ratios compiled from expense study are fitted to a distribution so tail risk measures could be calculated. Tails from both ends of the distribution are usually obtained. Sometimes a trend is also included in the fitting process.
- The RM impact is then captured for each assumption as the difference in modeled results between the model run with the BE and the model run with the stressed assumption. Both the upward and downward movement in the underlying variables are tested so the adverse direction could be identified.
- A correlation matrix between all underlying underwriting variables decided in Step 1 is also developed. This step can be carried out in step 1 and won’t probably be used in Step 2.
- A total impact of RM for all underwriting assumptions are aggregated, combining results from Step 2 and 3.
The process above describes a generic process on how the VaR RM approach is implemented. Other approaches could follow a different process.
Among the different risks, mortality and mortality improvement have been widely studied for a variety of reasons. Best estimate assumptions are typically based on tables and models published by research groups, such as the SOA. Insurers might adjust the assumption setting taking into account both the specific demographics of the policyholders and the results of their own experience study. As compared to other types of underwriting assumptions, e.g., partial withdrawal, practitioners rely more on quantitative analysis than qualitative assessment for mortality or longevity risks.
Quantifying the interaction between financial inputs and underwriting assumptions is more of an art than a science. It has been a while now, but I still vividly remember sitting in hours-long sessions brainstorming with colleagues the correlation matrix, covering all possible risk variables, for SII. Dynamic policyholder behaviors are very relevant to FIA. However, it is much easier to qualitatively assess the what-if scenario than to put a number around the potential reaction from the policyholder.
Conclusion
Most of the US domiciled insurers won’t have had to put together a holistic MCV framework for management reporting purposes, including pricing. The MCV framework is difficult to build up from scratch and it will involve a lot of effort. The good news is that the MCV concept is not new to FIA due to the investment components in its design, so some groundwork should already be in place especially around the modeling of financial assumptions. As external reporting standards such as LDTI and IFRS 17 push insurers to measure FIA on a market consistent basis, now is a perfect time for them to think about how to integrate the MCV framework into the management reporting and risk management. MCV framework can benefit the FIA issuers in many aspects, which makes the efforts involved to build out the MCV quite worthy:
- It provides transparency of risks in products from the product development stage as the implicit assumptions move to the explicit assumptions;
- it helps instill the culture of risk management from the beginning of the product cycle;
- it encourages collaboration among pricing, ALM and hedging, and other areas to ensure a robust measurement of risks and a fair price is charged for the risks; and
- it enables cleaner earning attribution analysis and variance analysis between pricing, hedging and valuation/external reporting should there be discretionary differences in methodology and assumptions.
Statements of fact and opinions expressed herein are those of the individual authors and are not necessarily those of the Society of Actuaries, the newsletter editors, or the respective authors’ employers.
Jing Fritz, FSA, MAAA, CFA, FRM, CERA, is a senior manager at PwC and a member of the Joint Risk Management Section Council. She can be reached at jing.fritz@pwc.com.