March 21, 2016

Improving the Return on Capital under the Solvency II Capital Requirement (SCR) Standard Formula using Market Risk Tail Hedging

Regulatory context and motivationSolvency_II_Optimization.png

Following an EU Parliament vote on the Omnibus II Directive in March 2014, the Solvency II Directive (2009/138/EC) came into effect on the 1st January 2016.  The capital requirement under Solvency II (SCR) is the capital required to absorb potential losses that the (re)insurance company could face over the next 12 months, under extreme situations (i.e. 99.5% VaR).  Indeed the overall management of these tail risk events is of primary importance for the insurance industry as such events can jeopardize profitability and even solvency.


In this short blog we focus on extreme market risk (MR) events, and more specifically discuss some key elements (re)insurers should bear in mind while trying to improve their return on capital under the SCR standard formula (SF)*  by adopting MR tail hedging strategies.


Appropriate market tail risk hedging instruments under the SF

The SF calculation of SCR can be described as the change of basic own funds (BOF) following extreme scenarios.  These scenarios are classified by risk type (Market Risk, Counterparty Default Risk, Operational Risk, Life Underwriting Risk, etc.) and each risk type is covered by a corresponding SCR module.  The SCR market risk module addresses**  Equity risk, Interest rate risk, Credit spread risk, Currency risk, Property risk and Market risk concentrations.


Therefore, in order for the market tail risk hedging strategy to improve the return on capital under the SF, it needs to specifically hedge out the extreme scenarios defined in the SCR MR module under the SF: fall in equities, large up and down interest rates moves, widening of credit spreads, etc.


The typical instruments one generally thinks of for market tail risk hedging are Out-of-The-Money (OTM) options, as they offer relatively cheap hedging for MR extreme events.  Hence an appropriate hedging strategy in our case would consist of buying OTM equity put options*** , payer and receiver swaptions, CDS call options, etc.


Compliance constraints of risk mitigation contracts under the SF

In order to be recognized risk mitigation contracts under the SF, these OTM options should satisfy different constraints.  Notably they should show enough liquidity, be traded with a counterparty with a high enough credit worthiness, be in force at the SCR calculation time and for at least the next twelve months**** .  For example as a consequence of the liquidity constraint a single name CDS option will probably not be eligible as a risk mitigation contract because of a probable lack of liquidity, whereas CDS options on indices like iTraxx or CDX will likely be eligible.


Points of focus when market tail risk hedging for capital relief purposes under the SF

When entering a long position in an index-based equity put hedge (whose index composition closely matches the equity portfolio composition), one expects at least to observe a reduction in the SCR MR Equity Risk sub-module. But, in order to make sure the introduction of this hedge actually provides overall capital relief, other elements have to be carefully considered by the (re)insurance company.


Firstly other SCR (sub-) modules may be impacted by the introduction of a hedging strategy, and to start with the Counterparty Default Risk (CDR) module. Indeed the bad news is that tail risk hedging with long OTM options under the standard formula will typically attract CDR capital, even if the options are perfectly (i.e. daily margin, zero threshold and zero Minimum Transfer Amount in the Credit Support Annex)  collateralized and in cash.  The reason is that in the SF a so-called “Risk Mitigation” component is added to the exposure in the Loss-Given-Default that is precisely equal to the capital relief brought by the OTM options hedges. Note that this regulatory feature enforces (over)-capitalization of the margin call risk inherently present in long OTM options positions.


Furthermore, one may need to pay attention to the SCR MR Currency Risk sub-module, e.g. in the specific case where trades in one currency are hedged by risk mitigation contracts in another currency (e.g. for liquidity reasons).  In this case, the hedging strategy will attract extra capital due to the Foreign Exchange risk.


Another important element of any risk mitigation strategy to look at under the SF is the basis risk.  For example, hedging the market risk of a given portfolio with index-based OTM options (e.g. Euro Stoxx/S&P 500) will most probably introduce basis risk since the composition of standardized indices is likely to differ from the actual names present in the portfolio.  A second example of basis risk arises when allowing interest rate swaptions to hedge the interest rate risk of bonds instruments.  Indeed interest rate swap curves and bond curves are not considered as two different risk factors in the SF, since the MR interest rate module only applies shocks to a unique “risk-free” rates curve per currency.  As a consequence under the SCR SF, the (re)insurance company is required to demonstrate that the basis risk is not material in comparison to the mitigation effect, otherwise it might face extra capital charge.  Notice though that some level of basis risk must be accepted by supervisors since perfect hedges are recognized to be often either not liquid enough or not economically sound.


Finally let us point out that setting up a hedging strategy based only on capital efficiency criteria under the SF would be dangerous from a pure risk management point of view.  Indeed the SF aims to capture the main risks that most (re)insurance companies are exposed to but may not cover all material risks a specific company is exposed to.  For example, there is no capital incentive to hedge the vega risk (i.e. the risk of losses due to changes in the volatility levels) in the SF.  On the contrary hedging the vega risk may even attract additional capital (e.g. through the MR module).  Hence when market tail risk hedging with OTM options a company may be left with the choice of either being capital efficient and leaving some open vega risk that eventually will materialize in Profit-and-Losses (P&L) volatility, or hedging the vega risk and accepting some additional SCR consumption.



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* Similarly to Basel II for banks, Solvency II has three pillars. The Solvency II pillar 1 framework establishes qualitative and quantitative requirements for the calculation of the SCR using either a standard formula prescribed by the regulators or an internal model developed by the (re)insurance company. 

** Notice that the inflation risk in Inflation-Linked investments is an example of risk not captured in the SF.

*** One could argue that buying protection (via e.g. CDS’s or CDS call options) may offer a cheaper alternative to equity put options (since credit spreads and equities have high negative correlation in tail events). But such a hedging strategy wouldn’t bring capital relief under the SF, since the different market risk factors (here equities and credit spreads) are not shocked simultaneously but separately in each SCR sub-module.

**** If a risk mitigation contract expires within the next twelve months, a prorata temporis capital relief approach must be taken, unless a rolling risk mitigation strategy is in place that has been properly defined in written in a policy and satisfies some conditions.




About the Author: 

Damien Lemonnier is a senior expert at Risk Dynamics, with a strong expertise in valuation models and XVA topics (CVA/FVA/KVA/etc). Damien is leading the Market Risk expert group that primarily focuses on building knowledge around current market risk topics of interest for our clients, e.g. return on capital optimisation via market tail risk hedging under Solvency 2, liquidity add-on models for CCPs, FRTB impact for CVA desks, etc. Click here to email Damien.


With the expertise of Céline Azizieh, Jérôme Barbarin, Aurélie Civilio, Cédric de Ville de Goyet and Tamar Joulia



Tags: Insurance


Damien Lemonnier

Damien Lemonnier

Damien Lemonnier is a senior expert at Risk Dynamics, with a strong expertise in valuation models and XVA topics (CVA/FVA/KVA/etc). Damien is leading the Market Risk expert group that primarily focuses on building knowledge around current market risk topics of interest for our clients, e.g. return on capital optimisation via market tail risk hedging under Solvency 2, liquidity add-on models for CCPs, FRTB impact for CVA desks, etc.