Solvency II and the search for the true discount rate

Authors: Servaas Houben

Pdf: The eternal actuarial struggle

Publisher, publication date: CFA UK Professional Investor , 2012


The eternal actuarial struggle –

Solvency II and the search for the true discount rate


The journey so far

Solvency II replaces the current Solvency I regime, which is based on prudent assumptions. Instead, Solvency II focuses on risk measurement and management, and applies market consistent valuation to assets and liabilities. One of the major differences between the two regimes is discounting of liability cash flows.

Why discounting matters

To ensure future payments to policyholders, an insurance company holds a best estimate reserve plus some margin, and an additional capital requirement: the latter is to withstand negative scenarios. All these three elements depend on the discounting method.

In the Solvency I era before the year 2000, interest rates were systematically above 3 or 4%, and a prudent discount rate of 3 or 4% on liabilities was assumed, resulting in relatively high reserve requirements (future cashflows being discounted with a low discount rate, resulting in a higher present value). However, after 2000 this prudent assumption turned out to be inappropriate, as yields declined, and the value of reserves appeared relatively low. Hence Solvency II decided to switch to a market consistent framework which applies actual instead of prudent yields for discounting liabilities, resulting in using a swap curve with credit risk adjustment. A similar development took place in the embedded value world where the traditional valuation method (TEV) was replaced by a market consistent approach (MCEV) in 2008.

Risk-free rate

The risk-free curve is used in insurance as a benchmark for discounting. Some practitioners make further adjustments depending on product type. The most common methods for applying a risk-free rate are either a government bond or a swap curve.

A government bond curve is considered by some practitioners to be risk-free as countries can generally raise taxes, reduce expenditures or print money (seignorage), and hence avoid a potential default. Also there tends to be more historical data for government bonds available making it easier to build a risk model required for capital calculations. However, a potential Euro crisis and Scottish independence might make government bonds less suitable for monetary unions, as seignorage is not always an option. Not only does a potential default complicate matters, but also different government discount rates for different countries within a currency union might be required (e.g. Eurozone) leading to arbitrage opportunities. Lastly the government bond market for smaller countries might not be very liquid, especially for longer maturities, and hedging could become more challenging.

There are several swap rate flavors available: LIBOR which involves some credit risk (which increased during the 2008 crisis) and the overnight rates either uncollateralized (SONIA), or collateralized (RONIA). The last two curves reduce the credit risk component. Swap curves tend to be very liquid, are available for longer maturities, many countries, and hence provide plenty of hedging opportunities. However, less historic data are available making calibration of the 99.5% Value at risk capital requirement less straightforward. Furthermore, due to the embedded credit risk the swap curves are not entirely risk-free.

As a result, some companies use swap curves for discounting their reserves, while using either government bond data or a blend of government bond and swap data for building a risk model.

The actuarial reflex and the birth of the liquidity premium

However, the economic landscape changed around 2009 and it became clear that valuing liabilities on a pure swap rate would lead to solvency and product profitability issues for certain insurance products. As in the previous Solvency I regime, the actuarial profession relied again on an adjustment, an actuarial reflex: the liability discount rate wouldn’t be independent anymore of the assets backing these liabilities, and hence assets and liabilities would move more in tandem with each other. In practice this implied that for products with predictable cash flow patterns, the insurer can back these liabilities by a corporate bond portfolio and hold these assets until maturity. Part of the spread can then be allocated to liquidity as corporate bond investors require a higher return due to higher bid-ask spreads in corporate bond markets.

Like in Basel II, Solvency II uses quantitative impact studies (QIS) to determine what the capital impact is of a proposed regulatory framework. QIS5 (2010) used the following approximation to estimate this liquidity premium (LQP), the part of the spread due to liquidity, on a forward rate basis:

LQP = Max(0, X% * (Credit Spread – Y%) + W%)

Equation 1


  • X% (50%): proportion of the excess spread over swaps due to illiquidity;
  • Credit spread: total spread in excess of swaps, either based on option adjusted spreads or asset spreads;
  • Y% (40bps): long term expected default;
  • W% (10bps): adjustment riskiness in swaps;
  • The credit spread changes over time while X%, Y%, and W% are assumed to be constant.

Furthermore, a different LQP was applied for different currencies depending on the duration of the corporate bond market. QIS5 applied the following assumptions (LLP: last liquid point. The longest term for which a full LQP applies):

Table 1: country and time dependent LQP

Table 1: country and time dependent LQP
Source: CFO/CRO forum

Lastly, LQP was assigned depending on product type:

Table 2: product depending LQPSource: QIS5 Technical specifications

Table 2: product depending LQP
Source: QIS5 Technical specifications

This led to a changing LQP over time which reduces the impact of spread widening, as a loss in corporate bond values is offset by a higher liability discount rate:

Figure 1Source: Iboxx

Figure 1
Source: Iboxx

Matching premium

The latest level 2 text assumes a matching premium (MP) instead which is calculated as follows:

Matching premium = (Yield asset portfolio – Fundamental spread – risk-free rate)

Equation 2


  • Fundamental spread = max (75% long-term spread over risk-free rate, expected historical default)

Contrary to the LQP there are quality requirements for the corporate bond portfolio: no assets may be invested in bonds lower rated than BBB, and there is an upper limit of investment in BBB-rated corporate bonds. Surprisingly, there are no restrictions for the duration of the portfolio of assets. Like the LQP measure, also the MP increases when spreads widen.

Figure 2Source: Iboxx

Figure 2
Source: Iboxx

Although the methodology hasn’t been finalized yet, it is already clear insurance companies will encounter several challenges:

  • Lack of credit data for non-US countries: the historical long term spread is available for US corporate bond data since the 1920s. However, corporate bond data are less widely available for other countries, making it more challenging for insurance companies to justify fundamental spread assumptions;
  • Asset mix quality requirements: to classify for matching premium capital reduction, an asset portfolio needs to pass the credit quality criteria over time. This poses a challenge for insurance companies to either invest in safe assets and avoid any forego (part) of matching premium benefits, or to invest in riskier corporate bonds, picking up a higher matching premium but facing the risk of ending up with a portfolio of insufficient quality;
  • Treatment of corporate bond-like assets: some property or mortgage products might portray a bond like payoff pattern and could therefore be considered as an appropriate investment for predictable cash flows. However, under the current framework these assets are not taken into account for MP;
  • Un-rated bonds: some loans to semi-government institutions may be un-rated and hence not allowed for under the current regulations;
  • Spread measurement: several spread measures are available (option adjusted, asset spread) and it is not clear which one will apply.

Opportunities for asset managers

The changing insurance regulatory landscape leaves plenty of opportunities for asset managers to reduce P&L volatility by creating financial products that:

  • Reduce the difference between SII discount curve and LIBOR curves;
  • Reduce the difference between the total spread and LQP adjustment;
  • Provide guarantees on the quality requirements on a corporate bond mix to qualify for Matching premium benefits.

Nevertheless, changing regulations have also resulted in insurance companies being very careful regarding their long term asset allocations (fear of regret): hence we might expect an increased demand for investment solutions once internal models have been approved as at 1 January 2016. In the meantime, the upcoming QIS6 study might provide more insight into the regulator’s perspective.



Barrie+Hibbert, Summary of Liquidity Premium Estimation Methods, October 2009

CEIOPS, Task Force Report on the Liquidity premium, 1 March 2010

CFOForum-CROForum, QIS5 Technical Specification Risk-free interest rates, 2 April 2010

European Commission, QIS5 Technical specifications. 5 July 2010

About Servaas Houben

I am a Dutch actuary and worked in the Netherlands for the first 4 years of my career. Thereafter, I worked for 2 years in Dublin and 4 years in London. I am now heading the actuarial department of ENNIA in Curacao.
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