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Fadai88
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VaR for a life insurance company

July 23rd, 2020, 2:59 pm

I'm not sure that my question belongs in here.

I need resources, recommendations for implementing VaR framework for life insurance business (credit risk, FX risk, interest rate risk etc). Could you please suggest any book, article, web resource etc? Does anyone have experience in development of VaR models for an insurance company?
 
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Alan
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Re: VaR for a life insurance company

July 23rd, 2020, 10:06 pm

a little search at amazon turns up at least one book with VaR and insurance in the title.
summer intern job?
 
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complyorexplain
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Re: VaR for a life insurance company

July 24th, 2020, 8:11 am

To answer your last question, I have considerable experience in VaR models for insurance companies, having worked as a specialist on the Solvency II capital project for many years. First thing to know is that insurance VaR models are not market consistent and often violate no-arbitrage, so do you want to know how insurers actually do it, or how they should do it? How they should do it is no different from how banks do it.
 
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DavidJN
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Re: VaR for a life insurance company

July 24th, 2020, 5:56 pm

complyorexplain - I'd appreciate more insight into the insurance mindset.  A few years ago, a Canadian bank failed miserably offering a deposit note that emulated a common insurance company product. The bank priced the note as they intended to replicate/hedge it, and the resulting pricing wasn't attractive. A sample of but one observation, but still it made me wonder about the degree to which the no-arbitrage replication paradigm has penetrated the insurance business on the pricing side.
 
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complyorexplain
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Re: VaR for a life insurance company

August 14th, 2020, 2:54 pm

David,

Sorry I missed your post above. Actuaries do not believe in risk-neutral pricing, so they use the 'P' method of valuation instead of 'Q'. A typical example is the actuarial pricing of equity release mortgages, where they calculate the forward price on the basis of predicted growth in property prices, which is completely wrong.

I was the architect of CP 13/18 before I retired from the Bank in 2018

https://www.bankofengland.co.uk/-/media/boe/files/prudential-regulation/consultation-paper/2018/cp1318.pdf

This was an attempt to make actuaries price options correctly (not sure it succeeded). The CP explains:

"(III) The present value of deferred possession of a property should be less than the value of immediate possession
 
3.16 This statement is equivalent to the assertion that the deferment rate2 for a property is positive. The rationale can be seen by comparing the value of two contracts, one giving immediate possession of the property, the other giving possession (‘deferred possession’) whenever the exit occurs. The only difference between these contracts is the value of foregone rights (eg to income or use of the property) during the deferment period. This value should be positive for the residential properties used as collateral for ERMs.
 
3.17 It is important to note that views on future property growth play no role in preferring one contract over the other. Investors in both contracts will receive the benefit of future property growth (or suffer any property depreciation) because they will own the property at the end of the deferment period. Hence expectations of future property growth are irrelevant for this statement."
 
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DavidJN
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Re: VaR for a life insurance company

August 17th, 2020, 2:47 pm

complyorexplain,

Thank you for that. As worrying as it is fascinating, A way's back, one of Canada's larger insurers got a bit shaky trying (or not, as the case might have been) to hedge such complicated products. The regulator's response at the time was to lower the capital bar for the sector and to force the large banks to provide it committed credit lines. It seems the mindset of the people doing the regulatory coverage is cut from the same cloth as that of the insurers.
 
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complyorexplain
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Re: VaR for a life insurance company

August 21st, 2020, 12:15 pm

"The regulator's response at the time was to lower the capital bar for the sector and to force the large banks to provide it committed credit lines. It seems the mindset of the people doing the regulatory coverage is cut from the same cloth as that of the insurers."

Sounds entirely right.
 
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Samsaveel
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Re: VaR for a life insurance company

August 23rd, 2020, 5:01 am

Two methods are common to calculate VaR (Full-revaluation & Taylor method ).  For the diffusion risks such as IR,FX,EQ, CSR ( credit spread risk ),COM(commodity), historical simulation (full revaluation ) VaR is the most used method.  You need at least 310 historical observations at the risk factor level.   For most risk factors apply relative shocks, for IR (negative ) apply absolute shocks. A combination of both methodologies applies to volatility surfaces for different asset classes ( strike, moneyness, delta, maturity and tenor ), apply different shocks to the wings & chest. For vanilla Fixed income portfolios where only first-order effects are dominant (i.e mostly delta risk ), to cut time, use delta of the portfolio as an approximation to your P&L instead of full -revolution VaR (Taylor method ),  and get the VaR from that.   For other risks that are not captured in your diffusion risks such as all trading book positions that are subject to own funds requirement for specific interest rate risk, except securitization positions and n-th to default baskets, use a type of credit VaR model in banking we call it the Incremental risk charge (IRC), captures losses that arise due to 2 types of risk ( migration risk & outright default ), over a one-year capital horizon, and 99.9% confidence level ( this model requires a lot of work and collaboration with your credit risk economic capital teams, banking book IRRBB teams and such to get the input to the model, e.g, issuer-issuer correlation matrix for underlying issuers, methodology for Probability of default, etc    These processes are very much involved and require an assessment of the liquidity of risk factors that goes into your VaR model because illiquid risk factors have to be captured in another model that works as an add-on to your overall market risk capital charge.  Anyhow, this is just a high-level taste of how to think about building a VaR model to capture market risk for trading book positions.  The actual work of arriving at the shocks per risk factor, full-revaluation of positions to arrive at P&L vectors, aggregation at desk level and trading book, backtesting, regulatory statistical tests to satisfy robustness of VaR model to regulators, etc.. among others requires continuous tweaks.   Also, given that facts on the ground show more occurrence of extreme events (jumps) or shocks, is VaR with the usual assumptions a good proxy for actual risk processes currently we are seeing in the Market!!
 
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complyorexplain
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Re: VaR for a life insurance company

August 24th, 2020, 8:33 am

@Samsaveel your points are correct for trading book VaR calculated for a bank. But insurance companies operate under the Solvency II regime, not CAD2 or Basel, and they tend not to have complex derivative exposures of the sort held by banks, although they do have embedded guarantees of various kinds, often of very long maturity. Plus a pile of credit risk. Needs a somewhat different approach, not that the current approach is anything like the right one.
 
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fyvr
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Re: VaR for a life insurance company

August 24th, 2020, 4:20 pm

The 'valuation under P or Q' issue is a tricky one, it might be clear for dealers (it's Q) but it's not at all clear for commercial exposures.
Suppose you are a commercial bank with a $100 million loan book, and the regulator says "what's your EL on a 5yr horizon?".  The correct answer depends on what follows - if the regulator is about to tell you to go out and hedge the risk with CDS, then you need to use Q; if you just want the 'best' unbiassed guesstimate of what your actual losses are likely to be (which will be < than number Q implies) it is perfectly reasonable to argue that the default rates you should use should be rooted in historical empiricals (i.e. P).
 
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complyorexplain
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Re: VaR for a life insurance company

August 24th, 2020, 6:57 pm

"it is perfectly reasonable to argue that the default rates you should use should be rooted in historical empiricals (i.e. P)."

I don't think so. See the sections of CP 13/18 on the irrelevance of P. It was a long and hard battle with the industry (and many actuaries) to get that paper out. 

https://www.bankofengland.co.uk/-/media/boe/files/prudential-regulation/consultation-paper/2018/cp1318.pdf
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