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### 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)

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

- 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

Gross premium

Calculation of insurance premium

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

- Classical life insurance pricing
- Profit testing
- Parameterization
- ABC&TC

- 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

- 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

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:

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.

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

5. Cash flow with mathematical reserve

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

RP Unit Linked product –company fund

Profitability measures

Benchmarks

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

- Classical life insurance pricing
- Profit testing
- Parameterization
- ABC&TC

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

- 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

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

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

- 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

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

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

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

- Classical life insurance pricing
- Profit testing
- Parameterization
- ABC&TC

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.

ABC method in the insurance industry

- Activities are composed of several tasks
- Activities are not necessarily separated organizationally
- Beware of the number of monitored activities

Business process elements

Process aspect

Cost drivers

Activities

Performance measures

Cost objects

ABM- ABC as the by-product provides information about the costs of individual activities in a business process.
- The use of this information and making business decisions based on such information is the basic concept of the activity based management (ABM).
- The ABM concept is used in different methods of cost management:
- Reduce costs,
- Activities based planning,
- Business performance measurements,
- Benchmarking,
- Reenegenering business processes.

Costs of claims

Actuarial model (profit test)

Insurance premium

Actuarial models for premium determinationThe link between profits test and ABM- Time component of cost
- Probability of the formation
- Cost amount

Actuarial models for premium calculationThe link between profits test and ABM

- The costs of activities are taken into account instead of the classical costs criteria.
- The probability of event is determined for the activities.
- The majority of activities are connected with the basis probability of the insured event.
- Activities are included in the profit test model according to the formation time in the life span of an insurance product.

Target costs - definition

1. The process of target costs is a system of profit planning and cost management that is:

- Price oriented
- Focused on costumers
- Focused on development, and
- Cross functional.

The concept of target costs initiates cost management at the earliest stages in product development and is used trough the entire product life span with the active involvement of the entire value chain (Anasari).

2. The concept of target costs in the insurance industry is defined as a comprehensive system of proactive cost management from the development of a new product to sales and marketing of the insurance product, or in the entire demand period for insurance services in terms of insurance admission, the insurance claims process and the customer support process. Based on the result that costs cannot be controlled with standard cost systems, as recognised by the market and the competition.

3. Target costs are different from the traditional calculation of costs plus in the way that the target costs are the function of the product’s market price, the desired profit and market share, and not on the contrary, that the selling price depends on the projected cost. With the target costs method the profit and cost structure of the product is determined, even before we start to its development.

The characteristics of target costs

- The price of the service determines the costs (the costs of claims and the operating costs) and not vice versa
- Customer oriented
- Focused on development
- Functional integration in the development of new products (important in the insurance industry)
- Orientation to the long-term cost management

- life insurance is a long-term contract

- Cost management in the entire value chain

Planning phase

Design and construction phase

Implementation phase

Testing phase

Target costs

The characteristics of target costs

- The premium sets the costs
- Orientation to customers
- Focused on development

The market price defines the develomplent of a new product

Meeting the customer’s expectations regarding quality, price and speed of service

The most costs of the products are defined during the development phase

Underwriting

Claims

Insurance administration

Informatics

Marketing

Sales

Law

Reinsurance

Multidisciplinary project group of the new product development

Target costs

The characteristics of target costs

Functional connectivity in development

- Planning a new product
- Determining target costs
- Determining the market price
- Determining the target profit
- Definition of target differences
- The use of techniques to achieve the target costs

Insurance conditions

Prototype 1

Insurance documentation

Prototype 2, …

Risk management

processing

Final form

Insurance premium

Initiative

Pricing strategy

Product concept

Market research

Realizability study

Endowment

(basic risks)

Marketing strategy

Amount of basic coverage

Premium payment method – free or bound

Profit sharing

Additional risks

CI

Waiverof premium payment in case of illness

Waiver of premium payment in case of unemployment

Additional accidence insurance

Protecting the family in case of illness

…

Option of retraining the insurance into insurance in perpetuity

Premature redemption

Premium return guarantee

Option of raising the insured sum in the event of childbirth

Insurance inactivity

Without medical examination

Planning a new product

Product development phases

Decomposition of insurance product

Competition

Value of detection

Loyalty

Quality and relative functionality

Price

MARKET PRICE

Reputation

Market share

Long-term profitability

Strategic goals of the company

Determination of target costs

Determination of market premium

- Key factors:
- Value of percetionof added options and functionality
- Brand power
- Target market share

Determination of target profit

- Net present value (NPV)
- Internal rate of return (IRR)
- Net present value share in the initial commission

Planned costs

Target difference

Cost analysis

Methods to reduce costs

Determination of target costs

Determination of target difference

To calculate the target difference it is necessary to know how much we spend today!

Example profit test

Costs of claims

Insurance premium

Determination of target costs

Decomposition of target costs in the insurance industry

Implementation of target costs

Methods:

- VE
- ABM
- Risk management
- BPR
- Benchmarking

- Two-stage implementation of target costs
- Manufacture of the product that will be as close as possible to target costs -> Analysis of value
- Design and implementation of activities associated with business processes -> ABM

(basic risks)

Amount of basic coverage

Premium payment method – free or bound

Profit sharing

Additional risks

Additional insurance for the risk of major diseases

Exemption of premium payment in case of illness

Exemption of premium payment in case of unemployment

Additional accidence insurance

Protecting the family in case of illness

Advance

Option of retraining the insurance into insurance in perpetuity

Premature redemption

Premium return guarantee

Option of raising the insured sum in the event of childbirth

Insurance inactivity

Without medical examination

Value engeneering

Desired properties of the product from the customer’s perspective

Functionality of the product

VE presents a systematic, interdisciplinary study of factors affecting the costs amount in a product, in order to determine whether it can be created at lower costs, without sacrificing the characteristics, functionality, reliability and usefulness of the product.

Safety for the family

Flexibility

Living benefits

Covering various life events

As little administration as possible

Implementation of target costs

ABM

ABM process

- Identifying the main activities in the company
- Allocating indirect costs to cost units of activities
- Selection of appropriate criteria of activities

Implementation of target costs

ABM

- The business of the company is viewed as a chain of related activities
- Obtain information about the main activities in the company
- Based on thus obtained information, we can eliminate unnecessary activities
- The basis for the use of different cost management techniques
- Primarily it is a activities management model within the company

Implementation of target costs

ABM

- Supplementing ABM and target costs
- In the insurance industry, we follow the process logic
- ABM follows the process logic
- When activities are cost categories, the target difference can be arrange more specifically
- By allocating target costs by activities, a more accurate picture can be obtained, where the target difference is formed
- ABM
- Specifies the target difference by activities
- By managing activities their costs are reduced

Value

Loyalty

Competition

Quality

Price

BSC (strategy, vision)

Reputation

Market share

Profitability

Procedures supporting the target costs achievement in insurance

ABC/M – activity analysis

Risk management

Redesigning business process

Benchmarking

Analysis of value

Quality assurance

The model of target costs in the insurance industry

TARGET PROFIT

MARKET PRICE

TARGET COSTS

Standard costs

Profit test

Target difference

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