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Swaps are used for hedging purposes against directional rates movements (insurance companies hold loads of fixed income instruments and are thus hugely exposed to overall rate levels, depending on holding period and portfolio turnover) and to insure against inflation (insurance firms receive fixed premium payments), to target portfolio duration This is ...


5

The publication is made by the UK institute of actuaries so I'm answering from the perspective of the insurance industry in the European union. Is it allowed? For European Insurance companies EIOPA gathers a number of statistics, among which asset exposures. The table below shows figures as of 2019Q4: So, at least for insurance companies that are ...


3

Insurers do use derivative pricing models such as Black-Scholes to price the sort of guarantees you describe. As far as I know, this used to be known as the "replication method" in the industry jargon, and it allows insurers to price guarantees in a market-consistent manner, hence enabling them to efficiently hedge them with traded instruments. In particular,...


3

It depends on the exact nature of the risk in question as well as the mandate of the options desk at the bank. Generally such products are "created" and hedged at exotic option sell-side desks. There are a myriad of different kinds of risk the bank and hence the insurance company may offer their clients insurance against. It could range from inflation risk, ...


2

In addition to what Matt Wolf pointed out, insurance companies use interest rate swaps to hedge certain liabilities arising out of their variable and indexed annuities business. It's somewhat dated, but this McKinsey report discusses those types of liabilities and how (if...) insurance companies hedge them.


2

An Insurance premium typically focuses solely on the downside of your Risk. An Insurance pays if you suffered some damage, but you do not give them some share of your profit if things are good. That means you have to get rid of the positive part of X, which has than of course a non-zero mean. Apart from that, I think you are correct, in that you can see $\...


2

Your link refers to a paper that compares the Standard Formula (prescribed approach to SII calculations) and Internal Models (where companies apply to use their own approach for deriving capital requirements). It is an old paper (2009). My suggestion would be to start by taking a look at the latest Technical Specs (30th April 2014) and navigate any ...


2

Depending on what the death rate is applied to (e.g. humans or butterflies or whatever...), the assumption that $m(x,t)$ is rather small compared to 1 is more or less valid. Assuming that this assumption holds, then both of your expressions for $q(x,t)$ would yield to: $q(x,t) = \frac{m(x,t)}{1 + 0.5 m(x,t)} \approx m(x,t)$, $q(x,t) = 1 - e^{- m(x,t)} \...


2

I think you will find little beyond the standard actuarial literature on the underlying contracts, which are really just XL covers. Since these contracts are written in non-liquid markets risk neutral or market consistent pricing is not highly developed or doesn't even make a lot of sense. In any way most of the information is proprietary and non-public. The ...


2

I'm not sure if this truly belongs in quantitative finance, but as an actuary, I can't resist responding. The answer to your question literally fills thousands of pages of regulations, research papers, best-practice articles, and study materials. Pension funds are VERY exotic options. They're not just puts. They're puts tied to mortality, employee behavior, ...


2

In addition to regulatory considerations for investments, the presence or absence of equity risk depends on the products sold. Two products which expose life companies to substantial equity risk are Variable Annuities or even just standard Unit Linked policies. Variable Annuities provide guarantees on equity funds. So they obviously create equity risk. But ...


2

this is classical Cramer Lundberg Model in ruin theory. In it the total number of claims is modeled using a compound Poisson process: $$ S(t) = \sum_{k = 1}^{N(t)} X_k, $$ where $X_1 \sim Exp(0.05)$. And the surplus is given by $$ U(t) = u + c \cdot t - S(t), $$ where $u$ is the initial surplus (in your case $u = 150$) and $c$ is equal to $15\%$. Part (a) ...


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The after-tax charge will most likely be a one-off charge of which the after-tax value is $6.2b, for example through an impairment.


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The only attempt at a comprehensive overview I know of is this book by the IAA (International Actuarial Association). A standard textbook on non-life insurance Loss models has a section on simulation. The excellent and comprehensive coverage in Quantitative Risk Management contains many implicit and explicit references to simulation. That said, most of the ...


1

A marine syndicate at Lloyds will insure 10 ships for 2018. The loss during 2018 on each ship will be $X_i$ for $i=1,\cdots,10$. The syndicate has limited capital and could be wiped out if the losses are too large. For this reason they may want to take out re-insurance. There are 2 kinds: (1) Stop-loss reinsurance puts a limit on the losses for the year, i....


1

I'm Phd student in insurance mathematics so I think I have a good position to answer your question. As you said, many insurance products have a financial component and an actuarial component, i.e. some financial guarantees upon the survival or death of the insured. Most insurance papers price this type of payoff via risk-neutral valuation. If you assume ...


1

While it seems surprising how longevity can be a risk, it becomes obvious if you look at the financial implications. For an individual longevity risk is the chance of outliving your retirement savings. For pension plans or more generally any financial institution guaranteeing individuals lifelong income, it is the deviation, due to increased survival or ...


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An interest rate swap can be regarded a combination of a floating-rate and a fixed-rate bond, with off-setting notionals: Pay-fixed IRS: we are short the fixed-coupon bond and received the variable-coupon bond. Since floating-rate bonds have very low duration (i.e. low sensitivity to changes in rates), being paid IRS means being short duration. Receive-...


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Here is another application. Suppose, an insurance company faces a wave of unexpected policy claims and issues floating-rate bonds to cover these claims. To reconcile the floating-rate receivables and fixed-rate payables, it purchases IR swaps.


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