Израчунавање премије осигурања живота

Израчунавање премије осигурања живота dr. Darko Medved Hotel „SLAVIJA“, Beograd, 9. i 10. decembar 2011. godine

KALKULACIJA PREMIJE • Insurance premium structure • Classical life insurance pricing • Profit testing • Parameterization • ABC&TC

Insurance premium structure • The insurance premium is a price for insurance service and defined by an insurance contract between the policyholder, the insured person and the insurance company. • The gross premium consists of the technical premium and the operating cost. The operating cost supplies the money for the exercise of the insurance business. The technical premium is the premium, intended for substituting claims, and is calculated according to the rules of actuarial mathematics. Operating fund Operating cost sum insured Risk premium Balancing risk sum at risk Gross premium Technical premium Savings premium Mathematical reserve Mathematical reserve 1….from savings premium and interest 2….covered from the risk premium

Elements that affect the premium • The amount of insurance premium is foremost dependent on the nature of the insurance coverage, included in the insurance contract. • The insurance premium is the function of general parameters, which determine the group of insurances in an individual insurance class, and special parameters, which finally determine the premium on the basis of an individual insurance contract.

Types of costs in the insurance industry The analysis of costs in an insurance company Cost of claims Operating costs Investment costs Interest costs Assessment costs Insurance acquisition costs Compensation costs Other operating costs Amortization of investment funds Labor costs Investment management costs Amortization Other costs

Types of costs in the insurance industry • Costs of claims present the category of costs, that are directly linked to the process of settling of the insurance claims. • Operating costs present in the strict sense the costs of the acquisition cost and other operating costs. • Acquisition costs cover the direct costs, linked to insurance admission: • Commission for insurance agents • Insurance underwriting costs • Costs of issuing an insurance policy • Advertising costs • Insurance acquisition costs present the majority of operating costs in insurance balance sheets, therefore insurance companies pay particular attention to these costs.

Distribution of cost structures • The following aspects must be considered in the cost structure of the insurance premium: • Technical aspect (actuarial aspect) • Customer aspect • Organizational aspect • Time aspect

Distribution of cost structures • Actuarial aspect • Basic insurance coverage • Additional benefits • Accelerators • Options (for example the option of increasing the insurance sum) • Guarantees (guarantees of rates, capital) • Customer aspect • The customer decision is made in terms of buying preferences (insurance premium: service) • The premium reflects the value of individual benefits in the eyes of the customer • Insurance as such have no concrete manifestations (selling an invisible product)

Customer support Development Marketing and sale Underwritingprocess Claims process Value chain Distribution of cost structures • Organizational aspect (value chain) • Aspect by business processes • Developing a new product • Marketing and sale • Underwriting • CSC • Claims process

Distribution of cost structures • Distribution of costs according to the time (time aspect): • Initial costs are costs, that occur in the first insurance years after issuing the insurance policy. • Adminstration costs are costs, linked to the maintenance and servicing of existing policies and insured persons. • Closing costs are costs, linked to the settlement of insurance claims. Time Time Costs Costs endowment annuity

Cost structure - example • variable cost = mainly connected with maintenance of portfolio • fix cost = does not depend on size of portfolio (management, IT) • initial cost: sales cost, development

Insurance premium structure • Classical life insurance pricing • Profit testing • Parameterization • ABC&TC

Classical calculations of insurance premium There are basically two approaches: • Classical calculation: • PV (premium) = PV (liability) + PV (costs) • Emerging of profit is not allowed (profit margin) • Surrrenders are not considered • Return on investment not considered • Cost of capital not considered • New business strain • Not possible for unit linked products • Profit test: • Discounted cash flow principle • Risk discount rate is considered • Basis for serious actuarial calculations of premium

Classical calculations of insurance premium • In the insurance premium calculations for life insurance it is important to remember that it must follow the principle of equivalence. • Principle of equivalence: The present expected value of premiums and payouts is equal to zero. • Random variable L is the variable of total loss of the insurance company. The technical insurance premium is obtained to satisfy the principle of equivalence. • Law of large numbers

Classical calculations of insurance premium • The present value of payouts of the insurance contract is Z. • K is the random variable of the time of payouts. • The expected present value of the random variable E(Z) is the single technical premium. • For example: endowment • Single premium

Classical calculations of insurance premium Technical premium • We define a new random variable L as the difference between the present value of payouts and the present value of premiums paid. • Thus chosen random variable may occupy negative as well as positive values, which presents a loss or a surplus for the insurance company in the sense of value. • The technical insurance premium is achieved by satisfying the principle of equivalence.

Classical calculations of insurance premium

Classical calculations of insurance premium Gross premium

Calculation of insurance premium A simple and generally understandable example of calculation of the technical premium for endowmnet life insurance.

Profit testing • Characteristics • Principle of discounted cash flow • Risk discount rate is being considered • Basis for any serious actuarial calculation of premium • For unit linked products the profit test is used • Key test for the decision to launch new products • Sensitivity of the parameters can be tested • Useful for target cost method • Appropriate set of parameters is very important • The technical composition of insurance premium is not important

Profit testing • 2. Parameters • Discount rate • Fixed costs per unit of product • Variable costs per unit of product • Best possible estimate of frequency and amount of claims • Surrenders • Investment returns • Cost of capital • 3. Expected cash flow

Profit testing Paid premium Pt Incurred costs at the beginning of the year - Et Interest earned (Pt - Et )*it Expected cost of claims - Dt *qx+t-1 Expected cost of survival - St *px+t-1 CFt is the expected cash flow for the insured person (x), still alive in the beginning of the year t:

Profit testing CFt = Pt - Et + (Pt - Et) it - Dt qx+t-1 - St px+t-1 Then we can define: ECt = CFt * t-1px , t = 1,2,..,n 4. Principle of equivalence On the day of issuing the policy the principle of equivalence must be used: Presuming: it = i.

Profit testing Principle of equivalence: the present value of cash flow from insurance policy must be equal to zero.

Profit testing 5. Cash flow with mathematical reserve

Profit testing 6. Measures of profitability Net present value NPV = Σ (1+id)-t t-1px PROt Profit margin Σ (1+id)-t t-1px PROt ------------------------- Σ (1+id)-(t-1) t-1px Pt

Profit testing Internal rate of return (IRR) Σ (1+iIRR)-t t-1px PROt = 0

RP Unit Linked product – Client fund

RP Unit Linked product –company fund Profitability measures

Benchmarks • term insurance – 10 to 18 • unit linked – 5 to 12 • endowmnet – 8 to 14

Parameters in determining the premium • Demographic assumptions • Return on investment • Costs • Inflation • Surrender • Safety margins • Expected profit • Risk discount rate (RDR) • Profit criteria • Net present value (NPV) • Internal rate of return (IRR)

Demographic assumptions • Mortality tables • Incidences of critical illnesses • Sickness tables • Annuity tables • Incidences must reflect the future expectations of individual risk for insured persons. • This values can be obtained by the transformation of standard population tables. • If the insurance company has enough data, it can include data from its claim experiance. • Alternatively, actual experience from comparable insurance class can be considered.

Demographic assumptions • For creating one’s own tables, homogenous data for a sufficient number of years is necessary. • If the insurance company has no appropriate data for making incidences, it is recommended, that they be made in the future. • If the company has no appropriate own data, the data on the level of the industry may be used, if it is available. • Data from reinsurance companies can be used. • Such an approach is recommended, if we are entering the market for the first time or if we have no experience with the new insurance class. • One’s own tables/incidences have to be constantly checked and supplemented.

Demographic assumptions - Analysis Factors affecting the actual incidence of mortality: • Age • Gender • Time period from beginning of insurance • Sales channels • Market segments • Cause of claim • Suicides

Return on investment To consider: • Long-term conservative expectations regarding each type of investment (shares, bonds,…) • The scope of investment guarantee  affects the type of investment in which the premium is invested • The impact of the expected investment return on the profits from the contract  the higher the impact, the greater the accuracy • The impact of the reinvestments of the existing investments • Expected investment mix for the product • The current return on the investment mix for the product • Types of investments (AFS, HTM, HFT)

Costs • Especially important, because it can significantly affect the profitability of the insurance contract. • Cost parameters have to reflect the expected costs through the whole insurance process. • Cost parameters are set for each insurance class on the basis of normal – theoretically justified costs. • Cost have to be determined on the product unit: • Depending on the premium • Depending on the insurance sum • In fixed amount • If the insurance company has no adequate data for cost analysis  analysis of similar products  using data on the industry level  reinsurance  detailed analysis of the processes and costs connected to them.

Costs • Including fixed costs presents a special risk  when the number of sold insurance at a fixed cost is estimated in the wrong way • Management, development and marketing costs are usually fixed costs • Fixed costs can be distributed: • As a fixed addition to the premium • Divided into classes according to the amount of the insured sum • The commission amount is usually the parameter that is set in the product development phase and presents the market price for the concluded insurance  information from market is important  reinsurance  experiences of countries with a comparable level of development

Inflation cost growth To be considered: • The current inflation rate  growth of retail prices  growth of wages • Expected future inflation rates • The difference between the return of government bonds with fixed return and government bonds with variable return • Medium and long-term economic forecast • Rate of economic development

Surrenders • The level of surrenders should reflect the expected development of insurance in future years • Experiences of insurance companies from the same or from similar products must be considered  the market  reinsurance • Calculating: • 1,2,3,6-monthly rate of resignations • 1,2,3,4,.. annual rate of resignations • Average 12-monthly rate of surrender: checking all insurance policies in our portfolio, when they were aged 12 months • Generational sustainability: checking all insurance policies, that were concluded in a given calendar year and are 12 months old 2009 2010

Surrender LR12 = AP>12 / ALLP>12 LR12 average 12-monthly rate of resignations AP>12 number of policies, older than 12 months, that were alive at the age of 12 months ALLP>12 number of policies that are or may be aged at least 12 months product idea! include this into pricing 8% 1 2 3 25

Surrender- Analysis Main factors affecting the rate of surrenders: • Time period from insurance entry • Sales channels • Market segment • Premium payment method • Type of contract • Terms of withdrawal/ exit penalties • Frequency of payment • Single premium / premium in instalments • Medical condition

Margins • The parameters are initially estimated as the closest approximation • When the profit test method is used in calculating premiums, the risk premium for future whitrawals from assumptions may be included: • through RDR • Including explicit safety margins on the parameters • When the premium is calculated based on a formula, the additions to the basic parameters are the only way to integrate risk premiums • Examples: • Mortality (10% do 20% loading) • Costs (10% on the best estimated cost) • A conservative rating of the number of sold insurance is assumed

Expected profit RDR • The owners decide where to invest their resources on the basis of: • Benchmarks • Risk investment rate • Mobility of the investment • Basic rule: the investor will require a higher expected return for more risky investments than for more secure investments  compensation for default risk • In other words, investors require a risk premium for the risk they assume • Also investors in insurance companies require a higher return than the return of risk-free securities; therefore the return: return on risk-free securities + risk premium

Expected profit RDR • The questions is, what is the appropriate risk premium in a life insurance company • RDR is not determined only by an actuary, the market also sets the return • At risk work RDR, it has to be considered: • Macroeconomic environment • Position of the company • Product complexity • Parameter stability in a product

Expected profit NPV • To optimize the NVP is the main priority of any manager • Is the best criterion of profitability • NPV can be presented in relation to the initial investment (for example commission) • NPV can be presented as a share of total premiums (prices) • Can be used for the initial assessment of the value of the company IRR • IRR is the interest rate, in which the sum of discounted future cash flows equals 0 • If all other assumptions are equal, the company should favour products with a higher IRR

Indirect costs First stage aloocation (cost drivers) Cost center of activity 1 Cost center of activity 2 Cost center of activity N Allocation of the second stage (activity drivers) Direct costs Cost units (insurance classes, customers, business processes, market channels) ABC method in the insurance industry • Important method in the insurance industry • according to research more than 52% of financial institutions in the UK use the ABC method • CEE is only at the beginning of this process

ABC method in the insurance industry • Method of calculating costs based on activities is a method that takes into account that costs arise as a results of activities, which are cost drivers. • The basic idea behind the ABC method is that costs are not caused by products and services, but activities, products and services are mainly the end result of such activities. • Activities consists of a concrete business process. • The ABC method is a two-steps calculation of costs : • In the first step costs are collected on the activity level, that are consolidated into activity based cost centres or cost pools; • In the second step costs from the activity based cost centres are arranged on cost objects; • The organizations is guided by the activity cost drivers or the activity criteria; • The activity criteria is usually set in quantitative units, not in units of value. • Cost objects in the insurance industry are products, clients, marketing channels, markets, individual processes and similar.

Израчунавање премије осигурања живота

Израчунавање премије осигурања живота

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