HiBrook financial advisors GmbH
HiBrook as Advisor
HiBrook offers advisory services to institutional investors, banks and building societies, as well as asset managers. Our advise expands across the areas of Risk Management, Asset Liability Management, Strategic Asset Allocation, Solvency II and Basel III, and for traditional and alternative asset classes.
HiBrook as Intermediary
HiBrook also operates non-licensed brokerage of advisory and administrative services in the ﬁeld of alternative investments and credit structures. The range of services is aimed at both product providers and professional and institutional investors from Germany and abroad.
HiBrook as bridge builder between services & solutions and the investor
HiBrook focuses on the investment needs of its professional clientele. Our aim is to offer high-quality advise and tailor-made solutions.
Independence & Transparency
HiBrook is managed by its owners and an independent company. For our clients we provide a high level of transparency both in the advisory as well as regarding the services procured.
The HiBrook team are looking at many years of experience in the asset management and the advisory of institutional clients and banks. Their expertise comprises the perspectives of both investors and product & solution providers.
Team & Competence
Dr. Christoph Püntmann
Ph.D., M.Sc. (Theoretical Physics)
OWNER, FOUNDER AND DIRECTOR OF HiBrook
Specialist for Asset Liability Management,
Structured Credit, Derivatives
Vita: Morgan Stanley, Goldman Sachs
Dr. Christoph Püntmann
Ph.D., M.Sc. (Theor. Physics)
FOUNDER AND PARTNER
ALM of insurers, banks, building societies, corporates
Solvency II, Basel III, internal models
Strategic asset allocation (SAA)
Derivatives (interest rates, credit, equities, FX, hedge funds)
Structured credit (CLO, ABS)
HiBrook, Frankfurt a. M. (Partner and Managing Director)
CIS Asset Management, Frankfurt (Managing Director)
Goldman Sachs, London and Dubai (Executive Director)
Morgan Stanley, London and New York (Vice President)
SciComp, Austin/Texas (FinTech)
Studies in Physics (Doctorate, Master), Austin/Texas, Marseille, Mainz
Specialist for Asset Management and
Vita: Sal. Oppenheim, J.P. Morgan, Commerzbank
Private Equity and Hedge Funds: Strategies and Asset Classes
Asset Management for Institutional Clients
Capital Market Strategies, Sustainability Strategies
Risk Controlling, Risk Management
Sales Alternative Assets
HiBrook, Frankfurt a. M. (Senior Advisor)
Sal. Oppenheim, Cologne and Zurich (Senior Vice President)
J. P. Morgan, Frankfurt (Vice President)
Bank in Liechtenstein, Frankfurt (Portfolio Manager)
Commerzbank, Frankfurt and London (Portfolio Manager, Banking Apprenticeship)
Diploma in Economics (University of Göttingen)
Senior Lieutenant (retd)
Dipl. Econ. Math. and Actuary
Advisor and Actuary to Insurance Companies and Pension Funds
Vita: Citi, Barclays, DZ Bank
(Business mathematician and actuary)
ALM of insurers, pension funds, pension schemes
Diploma in business mathematics, actuary (DAV), CFA (Level II)
Balance sheet and supervisory law, esp. additional interest reserve, Solvency I and II
Fund solutions, insurance products, structuring
Dalmis Investment and Risk Consulting (DIRC) - in cooperation with HiBrook
DZ Bank (Director)
Standard & Poors (Lead Analyst)
R+V Lebensversicherung (Trainee)
Accounting, Tax, Regulatory Reporting
Vita: Dresdner Bank, Fulda & Frankfurt
Masterstudent AI Engineering
IT, programming, database of HiBrook
Data protection officer of HiBrook
Solvency II: Internal model for CLOs
Collateralised loan obligations (CLOs) are securitisations of SME loans and fall under the category of asset-backed securities (ABS), which are issued in various tranches (from "AAA" to "equity"). They are a popular refinancing vehicle for loans of all kinds, especially in the USA, but have also become more attractive in Europe.
During the financial crisis, however, it was asset-backed securities that experienced particularly severe price distortions. However, not all ABS are equally risky. While ABS on subprime mortgage loans collapsed, almost all CLOs were able to fully service their cashﬂows during the financial crisis.
Collateralised Loan Obligations (CLO) are treated in the standard Solvency II model in the market risk module (Spread Risk Submodule). Solvency II argues that in order to hold an investment, an insurance company must hold at least enough capital to cover the loss of a 1-in-200-year event (0.5% VaR).
But this results in a signiﬁcant discrepancy between the credit risk on the asset side ("pool", "underlying"), which consists of leveraged loans (rated BB and B) and which is capitalised at approx. 30-40%, and the liability side of the CLO, which must be capitalised at 80-100%.
HiBrook has developed a partial internal model for the credit sub-module, in particular for structured credit, in order to better adapt the capital requirements under Solvency II to the actual risk profile (default risk, credit market risk, optionalities, reinvestment risk) of the ABS asset classes, in particular CLOs.
AA Tracker for Pension Liabilities under IAS 19
During the ﬁnancial crisis many pension schemes showed a high degree of fundedness due to high discount rates. Since then interest rates and credit spreads tightened strongly, leading to a signiﬁcant rise in pension deﬁcits. Furthermore, high volatility of the pension deﬁcit has potential capital implications on the corporate balance sheet. Hence, demand has been huge for an immunisation strategy, i.e. hedge, against the tightening and the volatility of the IAS 19 discount rate.
The rate at which post-employment beneﬁt obligations ("PBO") are discounted can be decomposed into the risk-free interest rate and a credit spread with AA-rating. Hence an immunisation strategy needs to address both aspects and both capital markets: Rates and Credit.
IAS 19 requires corporate pension schemes to be discounted at a rate "in reference" to a high-quality (i.e. AA-rated) corporate bond yield with currency and maturity commensurate to the pension liabilities. Accordingly indices such as the iBoxx EUR AA 10+ index have been deployed as discount rates. However, since the universe of AA-rated long-dated corporate bonds is very sparce with less than 10 debtors, the yield of the iBoxx index is primarily driven by heavy shifts due to drop-outs or newcomers to the index, which is an absolutely unhedgeable effect.
The AA-Tracker methodology was developed from the perspective of a liquid and investible index, which at the same time fulﬁlls the criteria under the IAS 19 rules as a discounting index. Hence the same index can be applied on both sides of the balance sheet of a corporate pension scheme allowing to immunise the volatile movements of the pension deﬁcit in a very elegant and sustainable fashion. Overlays in form of iTraxx and rates swaps & swaptions can also be used for managing the discount rate match.
Measurement of the illiquidity premium
Components of the return:
The return is divided into risk-free interest and risk premium. The risk premium ("RP") is primarily used to cover the intrinsic asset risk (default risk). The unexplained difference is then market-driven and can be identiﬁed primarily as compensation for holding the asset, the so-called "(il)liquidity premium" or "liquidity premium". The liquidity premium ("LP") is therefore not directly measurable, but can only be derived inductively. It is not to be confused with the costs of the transaction, which can indeed be measured. However, transaction costs and asset liquidity are correlated. In addition, for actively managed asset classes (e.g. hedge funds, CLOs), there is another source of return, the manager alpha.
Methods of measuring the liquidity premium:
It is true that "the more illiquid an asset class, the worse the data, the more difficult it is to measure LP." Most articles in the literature therefore deal with investment universes that are more liquid in nature, e.g. equities. In general, the literature on LP has two main focuses: Listed equities, because there is a lot of data available there, and hedge funds, because there illiquidity is made an asset class. However, if one wants to invest in non-listed alternative investments, but not only in hedge funds, it is difficult to describe a royal road for a comparable measurement of LP.
HiBrook has compiled in a study various methods of measuring the liquidity premium that we have identiﬁed so far and tested their applicability to a large universe of different asset classes. We would be happy to engage in a dialogue with you here.
Development of a capital market model
The objective is to develop a stochastic capital market model for application to asset-liability management and other applications to insurance companies and pension liabilities.
The model should do justice to its task and objective as far as possible, but without becoming too complex, according to the rule of thumb: "As simple as possible, as complicated as necessary." With increasing complexity, the effort for calibration and Pﬂege of the model increases disproportionately, while the additional gain in knowledge decreases. The model should be as simple as possible, but as complicated as necessary.
Among stochastic models, one can roughly distinguish two families:
- Econometric models ("Real World"), as they are applied in risk models, ALM models, collective models. Here, we understand risk models to be those fat-tail models that estimate not only the amplitude of the event (amount of damage) but also its probability.
- Arbitrage-free models ("Risk-Neutral"), which are indispensable for valuation models of structures and derivatives, and are suitable for optimisations of asset allocation.
In addition, there are of course also the deterministic single-scenario models, which ﬁnd application especially in stress tests for estimating the amplitude of the event with very simplistic probability estimation. The best-known example of this is Solvency II.
Other criteria to be considered in addition:
- Time horizon (e.g. 5-10 years for life, 1-3 years for non-life, 10-30 years for pensions)
- One- or multi-period time steps (e.g. quarterly or annual steps)
- Number of scenario paths (e.g. for optimisations rather less, for valuations rather more)
- Use of economic regimes with correspondingly different parameter sets
- Anﬂuss on accounting, e.g. through credit migrations, impairments, book vs. market value considerations
- Different currency areas, esp. if there is no currency mismatch
We also distinguish in the modelling of variables and their interrelationships:
- fundamental modelling (e.g. credit as a combination of bonds and equities),
- regression-based modelling, respectively based on the moments and covariances of the historical distributions.
Risk Retention Rule
Securitisations (ABS, RMBS/CMBS, CLOs, Auto Loans, Student Loans, etc.) represent a transfer of credit risk between issuers and investors. In order to prevent issuers from being able to dispose of unwanted risks at the expense of investors and to achieve an alignment of interest between issuer and investor, the risk retention rule was introduced for securitisations, which applies both in the new Basel III banking regulation, the Insurance Supervision Act (Solvency II), and in the KAGB for investments in investment funds.
The retention rule states that an investor may only invest in securitisations if the sponsor, originator or original lender retains at least 5% of the nominal amount of the securitisation at full risk itself, i.e. the party that usually derives the most benefit from the credit risk transfer.
Under no circumstances may the retention be resold, resecuritised or hedged in any way. At all times throughout the life of the securitisation transaction, it must be ensured that the 5% retention is retained as an own risk.
Affected market participants:
The retention rule focuses solely on the investor and does not restrict the investment itself. Investors include EU investors, including their non-EU subsidiaries, and the EU subsidiaries of non-EU investors.
The following sets of rules map the retention rule in the EU:
- KAGB/AIFMD (investment funds) since 22.7.2013
- Basel III (banks and credit institutions) since 1.1.2014 (Basel II par. 122(a) since 1.1.2011)
- Solvency II, ISA (insurers) from 1.1.2016
While capital-backed credit and insurance institutions will have to comply with higher capital adequacy requirements (banks: additional risk weight of 250%, insurers: full capital deduction), all types of investment assets covered by the KAGB will have to categorically unwind their positions in non-compliant securitisations over an 18-month window.
A market for non-compliant securitisations will still exist in which non-regulated investors can invest. However, this market will be much less deep, and will not lend itself as a settlement market for the regulated investors.
The retention rule can be satisfied by the issuer in various ways. However, for CLOs and most ABS, the "vertical slice" (pro-rata share in all tranches) and the "horizontal slice" (nominal weighted share in the equity tranche) are the most common. The retention can also be via a derivative, guarantee, surety or credit protection.
The deﬁnition of sponsor, originator and original lender does not automatically include the manager of the structure, unless the latter can assume one of the three roles.
In addition to a few EU securitisations that will no longer be compliant with the EU self-retention rule from 2015 onwards, it will mainly be most US securitisations that will not be issued with the EU self-retention rule in mind and will therefore also not be EU compliant.
The rulebook on the US self-retention rule is in preparation, but it is not expected to come into force before 2017. In addition, the US and EU retention rules are not compliant with each other, so US-compliant deals will not automatically be EU-compliant even after the US retention rule enters into force.
Fund for building society protection
The Fund for Building Savings Assurance ("FbtA") was created in 1991 with the aim of securing liquidity in the building savings collective for the allocation of loans. This was a consequence of the liquidity and allocation bottlenecks at German Bausparkassen during the early 1980s, which was mainly due to the very high interest rate level at that time.
Task of the FbtA
In addition to the liquidity risk in high-interest phases, low-interest phases represent an interest rate change risk that is probably just as high for the building society's business model. Due to the high redemption intensities and loan waiver rates to be expected in this scenario on the one hand and high continuation rates for savings contracts on the other, the interest result of the building societies comes under strong pressure here, even if at the same time there is sufficient liquidity in the collective.
The mechanism of the FbtA is to build up liquidity in phases of medium interest rates in order to be able to fall back on it in phases of high interest rates. In low-interest phases, however, the FbtA proves to be ineffective. The following diagram illustrates the interest rate dependency of the FbtA:
In a low interest rate environment, in which the investment ratio in the collective is very low and sufficient allocation funds are available, no withdrawals can be made from the FbtA.
In the medium interest rate environment, the extra-collective interest rate rises much faster than the inert collective interest rate, so that more allocations are made to the FbtA as the interest rate differential becomes positive and rises.
In the high interest rate environment, rising interest rates lead to a higher investment ratio and thus a decrease in available allocation funds. This can lead to non-collective borrowing to support the allocation and corresponding withdrawals from the FbtA to compensate for expensive reﬁnancing.
In the next diagram we show the mechanism of a convexity hedge, consisting of payer and receiver swaptions, so-called "strangle".
Comparison to FbtA:
- As with the FbtA, a cash outflow takes place in the mid-interest rate environment and a cash inflow in the high interest rate environment. However, the outflow of funds results from the option premium to be paid, while the inflow of funds results from the realisation of the fair value gains on the swaptions.
- While the FbtA is limited to the amounts paid in the past, the value of the option positions can (theoretically) be unlimited, which is why these are more like insurance policies.
- The "Strangle" is a symmetrical position and takes effect in both high and low interest rate periods.
In principle, it is conceivable to link the FbtA with a convexity hedge:
- The hedge could be built alongside the unchanged system of the FbtA.
- Future endowments earmarked for the FbtA could be invested in option premiums. The option hedge could be ﬁnanced from the FbtA.
The linking of FbtA and interest rate hedging would have the advantage that more building societies could hedge their interest rate risk specifically via the capital market.
 Der Langfristige Kredit: Immobilien & Finanzierung 14 - 2009; "Überlegungen zur Absicherung von Zinsänderungsrisiken im Bausparen"; Jürgen Steffan, Josef Schürle, Christoph Püntmann
 Bankmagazin 04 - 2010; "Protection for building societies to be supplemented by suitable instruments"; Jürgen Steffan, Josef Schürle, Christoph Püntmann
SAA vs. Solvency II
Both the Solvency II market risk module and the Strategic Asset Allocation ("SAA") are two relevant models in an insurance company ("IC") that have a signiﬁcant influence on the management of investments. They are based on different objectives, which may seem like massive inconsistencies when viewed superficially. Presenting these different objectives and debunking the resulting inconsistencies was the aim of a study by HiBrook.
Properties of the models
Solvency II market risk module:
- Risk model, only for modelling risk, not return. It represents the 1/200 year event, not normal operations.
- Market risk module consists of 6 sub-modules on market price risk (interest rates, equities, real estate, spreads, concentration risk, currencies), which are added together by a fixed correlation matrix.
- Market price shocks derived from historical distributions of representative market indices, partly with procyclical adjustments
- Duration weights for interest rates and spreads; rating weights for spreads
- Internal models possible to more adequately represent the risk proﬁl of the individual capital investment.
Strategic Asset Allocation ("SAA"):
Optimising return to risk
Risk usually measured as volatility or standard deviation (i.e. expected value of deviations); return as expected value. One optimises in the space of expected values, i.e. current operations.
Extreme value risks (e.g. 1/200-year event in Solvency II) represent a boundary condition for optimisation. An iterative reconciliation between optimisation and stress test can be developed from this between SAA and risk model.
Return, risk and correlations between asset classes are usually derived from historical time series that adequately represent the capital investment.
- Correlation matrices: The correlation matrices used by Solvency II and the SAA differ greatly. What may seem inconsistent at first glance is not in itself a contradiction. On the one hand, the correlations depend on the choice of risk measure (0.5% VaR for Solvency II; standard deviation for the SAA), i.e. the more extreme the market event, the higher the correlations as a rule. On the other hand, they also depend on the choice of index time series. While in Solvency II the shocks and correlations have been derived from indices, these are pan-European and fixed until further notice. With SAA, indices are used that are speziﬁsch adapted to the capital investment of the institutional investor and can be regularly reviewed and changed.
- Internal models: Solvency II also allows internal models for asset classes, where the institutional investor can better align risk capital with its core asset classes. In many respects, this then approaches the modelling under the SAA, as the same indices can be used as a basis here. However, internal models are very costly and have to be approved by the supervisory authority.
- Optimisation: The optimisation ﬁnds in the SAA under the measures "return" and "volatility". The stress tests according to Solvency II "only" form a boundary condition. It would not make sense to carry out the optimisation in the Solvency II risk measure, since the stress case ofﬁcially only takes place every 200 years (0.5% percentile). One must pass the stress case, but not be in an optimal position. Moreover, "optimal" in one risk measure (e.g. 0.5% VaR) is not necessarily optimal in another risk measure (e.g. standard deviation). In contrast, it makes a lot of sense to optimise in the environment of expected values (i.e. SAA) because that represents the "expected" case of insurance operations.
- Duration: Duration plays a major role in optimisation. Depending on which forward interest rate scenario one uses, duration can systemically favour (falling interest rates) or disadvantage (rising interest rates) annuities. There are basically three ways to deal with this: - One consciously accepts the effect, e.g. if one has a clear opinion on the development of interest rates. - You can neutralise the duration by choosing a ﬂat forward interest rate scenario or by freezing the allocations to bonds. In this way, the duration carriers still have an influence on the other assets in the optimisation process. - Duration can be removed by means of a swap. But then one must consequently swap all duration carriers, not only government bonds and Pfandbriefe, but also credits with their shorter maturities.
- EUR decay: EUR decay is a signiﬁcant extreme value risk. If, under Solvency II, the EUR decay of all investments in non-DEM currencies had to be backed by 25% equity, this would not be ﬁnancially sustainable for the normal German institutional investor. Here, however, it is dangerous to demand backing according to Solvency II. Firstly, those who actively measure this risk put themselves at a disadvantage, because Solvency II then requires them to back it up. Secondly, if the EUR collapse should actually occur, a political solution will be found, as all German insurers will have exactly the same problem. In this respect, it is a risk outside the scope of Solvency II.
- Diversification: The measures of return x vola are too few in optimisation to truly represent all asset classes in a sustainable way and make them comparable. For example, a niche asset class such as private equity may have a very good proﬁl under this measure, but may have unacceptable risks at the extreme (e.g. 0.5% percentile), which is not sufficiently taken into account by the standard deviation. Therefore, it is generally recommended to consider all asset classes and to drive a broad diversiﬁcation.
Measures in the low interest rate environment
In the current low interest rate environment, insurers and pension funds are finding it difficult to invest in appropriate safe assets to service the guaranteed interest on their contracts. Accordingly, we would like to discuss here 12 measures that can also be quantiﬁed in the individual case.
Contribution development ("CD"):
The premium development refers to the classic guarantee contracts in existing business, some of which were still written at high guaranteed interest rates ("GIR"), but which can no longer be earned with the interest rates on the market. The guarantee claims also refer to future current premiums and special payments for the contracts concluded.
Incentives must be correctly set for the sales department so that it does not recommend customers to pay premiums into the high-interest contracts instead of into the more market-compatible neutral tariffs. Control by means of an appropriate commission model and the corresponding placement of advertising as well as appropriate communication with the sales department are appropriate here.
Capital amortisation ratio ("CAR"):
The policyholders ("PH") have the option of having the accumulated capital paid out immediately upon expiry of the entitlement instead of life-long pension payments. The problem for the pension fund is that the lifelong pension payments also continue to accrue interest at the high GIR rate, which would be eliminated by a lump-sum payment. In the event of a continuing low-interest phase, however, the economic motivation of pension members for a lump-sum payment is likely to be relatively low.
The measure here consists primarily of communicating to policyholders and bringing about an active decision for or against the capital termination. Due to the individual life situation, it may be advantageous for the individual PH in individual cases to draw the capital termination option. Therefore, the prospect of increasing the CAR for the customer exists solely on the basis of appropriate selection, communication and advice together with an individual profitability calculation and presentation. In addition, the customer's willingness to sell capital can be incentivised by appropriate incentive models (e.g. bonuses, fee-free settlement).
Caveat: The legal and reputational risks are absolutely paramount in communication. Here, the appearance of an advantage must not be created by the capital abﬁndation if the customer would otherwise be clearly disadvantaged. It is also advisable to know the tax advantages and disadvantages and to explain them to the client accordingly.
The typical I of a German pension fund is in bonds with a high credit rating (government bonds, promissory note loans, registered bonds, Pfandbriefe). However, current market yields no longer allow the guaranteed interest to be earned on the insurance contracts.
The objective is to increase the average return of I without a signiﬁcant increase in risk. This can be achieved by appropriate admixture of a risky income portfolio (shares, alternatives, credits), if the risk is balanced by the simultaneously higher diversiﬁcation in the investment portfolio.
Provisions usually represent the largest cost block of the company. Here, a commission model must be set up accordingly and possibly renegotiated, which will incentivise neutariﬂiche contract conclusions and at the same time allow the pension fund to remain competitive. Commissions on high-interest legacy contracts should generally be nulliﬁed.
Costs of administration ("COA"):
Administration of the company and capital investment also represent large cost blocks. Here, processes and structures need to be reviewed accordingly and ggﬂs. outsourced or renegotiated.
New business ("NB"):
New business is the future of the company. Here, a suitable, competitive tariff structure must be set up and the incentives of distribution must provide the appropriate incentives.
Unless the pension fund is in a state of liquidation anyway, in which case there would be no need for NB and the saving of commissions.
Additional interest reserve ("AIR"):
For the old portfolio, the calculation of the AIR in accordance with the German Ordinance on Actuarial Reserves ("DeckRV") does not apply directly. This must be agreed with BaFin directly and on a case-by-case basis. The withdrawal from the provision for premium refunds ("RfB") can also be included. The AIR for the NB according to DeckRV, on the other hand, is non-negotiable.
One measure may be to modiﬁcate the AIR of the regulated old portfolio through negotiations with BaFin, e.g. by smoothing the interest rate curve or lowering(?) the reference interest rate.
It is of course questionable to what extent and how often BaFin would be willing to accommodate the PF with such concessions. The PK's intervention is thus relatively limited.
Interest rate assumptions:
The assumption of the expected interest rate development has a decisive influence on the calculation of the PF's own funds. Basically, there are two basic approaches that can be taken here:
(1) Near-market interest rate scenario: Forward interest rates based on the currently traded yield curve. These forward rates represent the price at which one can lock into an interest rate today in the future. Forward interest rates are also often regarded as the "expected" and thus "most probable" interest rate scenario. Only, forward rates have the disadvantage that this "most likely interest rate scenario" changes with every small movement of the yield curve (in a leveraged way) and is thus extremely unstable.
(2) Fundamental interest rate scenario: Here one can take the historical average or an economically plausible interest rate target. This interest rate target can also be a stress scenario, which the PF should pass in any case. The advantage is that this scenario has to be justified, but not constantly adjusted, which leads to a corresponding stability of the results and the capital requirement. Interestingly, it is also possible to calculate a break-even interest rate scenario in order to determine at which interest rate increase the own funds requirement is stabilised or neutralised.
Realisation of hidden reserves ("ROHR"):
Rapidly rising interest rates pose a major risk, as this would mean that the hidden reserves for realisation would no longer be available for the AIR.
Surplus participation ("SP"):
The new Minimum Allocation Ordinance ("MindZV") with publication of the Life Insurance Reform Act ("LVRG") of 6 August 2014 stipulates that only a maximum of 90% of KA income less GIR expense, but at least zero, must be allocated to the RfB. This new formula leads to a lower company burden in times of low investment income.
According to the new Minimum Capital Requirement Ordinance, at least 90% of risk profits (biometric profits) are allocated to the reserve for premium refunds and at least 50% of other profits are allocated to the reserve for premium refunds (instead of 90% of all profit sources as before). The own funds requirement can thus be significantly reduced if this limit is actually exhausted in the SP.
Lowering the guaranteed interest rate:
According to Par. 314 VAG, it is possible to reduce the minimum interest on the accumulated policyholder credit balances of already existing contracts for future years (i.e. reduction of benefits) if the PK can prove to BaFin that it is unavoidable for the survival of the collective. In our opinion, this step can be taken as a "strategic measure", which acts as a one-time control variable. However, this step will be taken as a very last resort because it can be reputationally damaging.
Cancellation Quota ("CQ"):
Cancellation is mainly known from the life insurance sector and is usually accompanied by high discounts on the surrender value. Cancellation with individual life insurers usually depends on the individual life circumstances of the PH, which is correspondingly independent of the interest rate level in the case of non-rational exercise behaviour.
In the case of occupational pension schemes ("bAV"), however, the lapse rate plays only a very subordinate role, since the contracts can be made non-contributory at most.
Additional interest reserve
The additional interest reserve corresponds to the difference between the actuarial reserve and the comparative actuarial reserve. The comparative actuarial reserve, which is not determined collectively but on an individual contract basis, is calculated with the help of an interest vector from one-year forward rates that are equal to the minimum of the reference interest rate on the balance sheet date and the contractually agreed actuarial interest rate for the respective year for the period of the next 15 years. Thereafter, the forward rate is equal to the contractually agreed actuarial interest rate. As a result, benefits and contributions will be valued with term-dependent zero rates from year 16 onwards.
Özcan Dalmis et al, "Financing the additional interest reserve", Der Aktuar 04/12
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