The previous section dealt with the concept of insurance pricing. This section will deal with the pricing procedure, and its determination.
Basically, pricing procedure is a methodical and sequential use of technique to determine the right price of the product. The insurer can determine the pricing procedure based on Sales area
(Sales Organisation, Distribution Channel, and Division), Customer Pricing Procedure (CPP), and Document Pricing Procedure (DPP).
The following elements are considered while pricing insurance products:
Claims cost – It includes claims paid in conjunction with settlement expense, estimate far outstanding claim, and so on.
Business acquirement cost – It includes commission, brokerage and business development cost, and so on.
Management expenses – These include salaries, rent and other expenses necessary for managing an organisation.
Profit – It include return on the capital cost.
Pure premium method
The pure premium is the average loss per coverage unit, or in particular, the product of the average severity and the average frequency of loss.
The average frequency of loss (F) is obtained by dividing the number of losses invited (NL) from the number of coverage units (NE) in the appropriate class. This concept is used to calculate the
average number of losses for all insured.
The average severity loss (S) is obtained by dividing the monetary amount of all losses (SL) from the number of losses invited (NL). It represents the severance of the loss.
Thus, the pure premium is determined by multiplying the average frequency of loss and the average severity of loss, but it reflects the average loss of insured expectations. In order to meet
all the losses, each insured who are involved in the particular class of business must pay the amount before commissions and administrative expenses.
Pure Premium (PP) = (average frequency of loss) * (average severity of loss)
PP = (NL/NE) * (SL/NL) = (SL/NE)
These concepts can be used to determine the losses, but they do not consider the distribution of losses. Thus, the pure premium distribution is defined as the probability distribution of total
losses for an appropriate class of business.
A measure of the intrinsic variation in the population is the variance represented by:
σPP2 = Σ (PP – μ) / (n-1)
Where, μ = theoretical pure premium distribution mean.
However, the marketing manager refers only a sample but not the entire pure premium population. Thus, while estimating μ they are expected to refer to the true value.
Assume that the insurance marketing manager refers to a sample randomly from the basic pure premium distribution. Then, it shows that the average losses for a sample of n coverage units
follow a normal distribution. In other words, if they refer random samples continually then it represents the average or mean of the sample pure premium follows a normal distribution. Thus,
the standard variation or error of the mean of a sample pure premium distribution (σm) is defined as the standard deviation of the pure premium population distribution adjusted by the number of
coverage units and is given by,
σm = σPP / √n
The calculation of standard error of the pure premium distribution is necessary because the average pure premium is incremented by a risk factor that compensates the error to the expected
variations in the productivity.
In addition, the accuracy of the estimation increases with the increase in the number of coverage because the standard error of the average of the pure premium decreases with the increase in the
sample size.
Two other factors also come into picture during the estimation of pure premium, which are credibility factor and loading factor.
Credibility factor refers to the extent to which an experience of an appropriate insured considered in the pricing process. It refers to the amount of confidence of the price-maker (marketing
manager) to show that the available data represents the losses to be expected in the future accurately. Thus, the equation for the acceptable pure premium is given by,
PPacceptable = (C*PPi) + ((1 – C)*PP)
Where, PPi = pure premium derived from the experience of the insured.
PP = pure premium derived from the experience of the actual population.
C = credibility factor, 0 ≤ C ≤ 1
Loading factors refers to the transaction expenses and the profit margin expressed in terms of percentage. Taking into account the traditional issues in concern with the economic objectives of
regulation and the fair price discrimination, the gross premium value is determined by using the equation,
Gross premium = Pure premium / (1 – loading factor)
The pure premium can also be determined as follows,
Let,
The costs of set of events to be covered for an individual on yearly basis,
{c} = {c1,c2,…,cn}
Probabilities that occur for each events in a year, {p}={p1,p2,…,pn}
The risk function of this insurance policy be X. Then, X(ci) =pi
Group of persons insured, {H} = {1,2,…,h}