Pricing uncertainty: Ignore volatility at your perilThe combination of a dozen or more models could lead to some very uncertain point estimates Pricing uncertainty: Ignore volatility

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Pricing uncertainty: Ignore volatility at your peril

Current Issues in General Insurance2nd May 2013

About the presenters

Sherdin Omar is a senior manager with Ernst & Young’s European actuarial services practice. He has significant technical and commercial motor insurance pricing experience building predictive models for motor and home pricing as well as managing the pricing structures for one the UKand home pricing as well as managing the pricing structures for one the UK leading motor brands. He has advised a number of leading motor brands on a wide range of projects ranging from getting value out of data and elasticity.

[email protected]

Dr. Ji Yao is a manager with Ernst & Young’s European actuarial services practice. He has extensive experience in various modelling for pricing with a solid background in mathematics and statistics. He has extensive first-hand gexperience in risk models, demand models and price optimisation. Recently, he has worked on elasticity modelling for a large insurance-related company.

[email protected]

2 Pricing uncertainty: Ignore volatility at your peril

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Agenda

Background

D ibi i i t i t d dDescribing pricing uncertainty and adequacy

Quantifying pricing uncertainty

Applications of pricing uncertainty

Summary

Q&A


Background

Motor insurance results seminarPage 4

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Pricing is the primary lever that affects revenue and ultimately profitability

Pricing: Sets maximum available profit

y s

available profit(includes ancillary income)

sInvestment returns

nal

es

Po

licy

proc

es

5

Once a policy is written, there are limited levers an insurer can use to influence the final profit for that business

Cla

impr

ocesResidual profits

Pricing uncertainty: Ignore volatility at your perilO

pera

tioex

pens

e

The UK insurance market is one of the most competitive markets in the world

80%

90%

o

Motor Home

100%

110%

120%

130%

Rep

ort

ed n

et c

om

bin

ed r

atio

6

Source: S&P and Ernst & Young interpretation

Year

Please note all results are before ancillary income and investment returns


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140%

150%

3,000,000

3,500,000

Case study: A UK motor insurerCompany maintained premium volume but grew customer numbers, while the performance deteriorated

The company maintained premium volume but

90%

100%

110%

120%

130%

500,000

1,000,000

1,500,000

2,000,000

2,500,000

Rep

ort

ed n

et c

om

bin

ed r

atio

Gro

ss w

ritt

en p

rem

ium

(£k

)

pgrew customer numbers, while the results deteriorated

80%02005 2006 2007 2008 2009 2010 2011

Year

Gross written premium Reported net combined ratio

7

Source: S&P and Ernst & Young interpretation


Any company’s data only represents a small proportion of the market

►Remember that the best estimate is only a point estimate from the sample of the total

Company A10%

Company B8% Company C

20%Company D

6%

market

►Typically, the standard error of predicted values is related to the sample size

►where s is the sample standard d i ti

Whole market

%

C ACompany B

Company C

Company A has grown by moving into new customer segments where it has no

historical data. Its pricing decisions have been based on extrapolation

deviation

►n is the number of observations

8

Whole market

Company A20%

6%Company C

18%

Company D6%Can Company A be sure it has grown in

a sustainable fashion with accurate pricing?


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Looking at multiple factors at once, there is limited data to support pricing in the potential growth segments

►30% of book is non-core segments2500

3000

3500

cies

Distribution of age by car age by NCD

Non-core customer segmentsPotential growth customer segments

Core customer segments

g►Under-pricing these segments by 5% will lead to 1.5% increase in loss ratio of total book

► Pricing models will extrapolate the experience from the core customer segments into the potential growth customer segments and non-core segments

0

500

1000

1500

2000

Nu

mb

er o

f p

oli

c

Age by car age by NCD

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► The less data available in these segments, the greater the uncertainty in the predicted values► For example the pricing models become increasingly unreliable as we consider the customer segments

to the right► The key issue is how much reliance is placed on these predicted values?

► For smaller companies, these issues could arise in some two way interactions.


Creating a rating structure is a combination of science and art

► Typically we use science (statistical models) to set the relativities for the technical price

► And overlay ‘art’ to set the future claims and premium assumptions to calculate ‘street price’

► However are we considering the volatility in our models?

► Is that volatility significant ?

► What could we do about it?


An insurer that understands the volatility in their pricing models should be able to gain a long term competitive advantage

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Describing pricing uncertainty and adequacy


Key discussion point is to identify and apply pricing uncertainty into the pricing decision

Hypothesis► Each insurer’s own experience is only a sample of the overall market experience for any risk► The smaller the sample the higher the risk of mispricing► Over-pricing: potentially profitable business is lostp g p y p► Under-pricing: has the potential to be a significant issue, especially on a price comparison

websiteChallenges► Competitors may have lots of data for a

specific segment, but you do not► How much to adjust the basic risk price by

customer segment to allow for sample error.► Checking that the under-pricing risk across

the portfolio is within the insurer’s risk

Risk premium calculated by insurer A

Insurer B estimates the risk cost to be less than insurer A.However there is a 45% chance that the actual risk cost is greater than insurer

Risk premium calculated by i B the portfolio is within the insurer s risk

appetite.► Putting in place real-time portfolio

management.

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A’s view.Is Insurer B under pricing?

Potential range of expected risk cost

insurer B

45%


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A typical approach to risk cost modelling ignores the uncertainty associated with each component model

Risk premiumThe important thing is to quantify the uncertainty when the component models are combined to aid the pricing decision

AD BC

AD Freq

AD Sev

Large BI BC

LBIFreq

LBI Sev

Small BI BC

SBIFreq

SBISev

TPPD BC

TPPD Freq

TPPDSev

WS BC

WSFreq

WSSev

F&T BC

F&TFreq

F&TSev

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q q q q q q

► Each model (frequency and severity) has some uncertainty associated with it► Typically this uncertainty is ignored► The combination of a dozen or more models could lead to some very uncertain point

estimates


Result of bootstrapping: the estimated burning cost can have significant variation

200

250

360

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400

2% difference Where there is less data, the variance is

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mb

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ies

(th

ou

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ost

9% difference

significantly larger

0200

220

0-1 2 3-4 5-6 7-8 9+

No Pols Selected 95th percentile 5th percentil

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Tenure

5th percentile


Number of policies

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In our potential growth segment our estimate

How does the range of the prediction intervals vary with the number of policies?

40

50

60

ere

nti

le –

5th

ti

ca

l po

lic

ies

Graph showing the variation of risk premium

Non-core customer segments

Potential growth customer segments

Core customer segments

gcould differ by in excess of ± £10, which will make a difference in highly elastic marketsFor non-core customer segments the results are highly uncertain

0

10

20

30

40

521

282

070

239

844

239

121

819

534

981

401

355

249

221

197

140

129

100

93 85 21 19 10 6 5

Bu

rnin

g c

ost

ran

ge

(95t

h p

ep

erce

nti

le)/

nu

mb

er o

f id

en

Range

Graph showing the variation of risk premium when there is sparse data

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The potential growth customer segments have enough uncertainty to skew predicted results significantly, while the non-core customer segments have a wide uncertainty on predicted results

195

112 40 32 28 12 11 8 5 9 4 3 2 2 1 1 1 1

Number of identical policies


The scope to reduce price in potential growth customer segments is limited by pricing uncertainty

Core customer segments Potential growth customer segments

9,00010,000

8 0009,000

10,000Best estimate of burning cost

Best estimate of burning cost

Range of best estimateRange of best estimate

01,0002,0003,0004,0005,0006,0007,0008,000

400 450 500 550 600 650 700

Dem

and

Premium (£)

01,0002,0003,0004,0005,0006,0007,0008,000

400 450 500 550 600 650 700

Dem

and

Premium (£)

Current price

burning cost burning cost

Current price

►Price is set with a margin to the burning cost


►Price is set with a margin to the burning cost but is already competitive►To increase sales in this segment efficiently, a combination of price, product and marketing is needed

and the price is not competitive►A small change in price is expected to grow volumes significantly►Due to the uncertainty of the burning cost we need to understand for which customers within the segment we can reduce the margin

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The uncertainty around the burning cost prediction can be explicitly calculated

► Let and be the linear predictors of the frequency and severity models, respectively.

► The 95% confidence interval of the burning cost is defined as:

► The covariance is computationally difficult to calculate, so let

► So the 95% confidence interval is simplified to


The simplification holds true against the results from the bootstrap exercise► We can ‘measure‘ the uncertainty around the burning cost using confidence

intervals with a simplification for independence.

► The results are similar to those obtained from the bootstrap, except when the

uncertainty is very large in which case we over estimateuncertainty is very large, in which case we over-estimate.

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un

cert

ain

ty

Theoretical vs empirical uncertainty

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0 50 100 150 200 250 300 350 400 450 500

Th

eore

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Empirical uncertainty


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Applications of price uncertainty


We reserve to a defined percentile. Should we also manage our prices actively to a level of adequacy?► Let’s define Pricing Adequacy (PA) for a policy as

where,

P i th i f th i kP is the price for the risk

PL is the lower bound of the burning cost estimate

PU is the upper bound of the burning cost estimate

Example

► The current price for this risk is £300

► For a nominal 10% increase we can increase the pricing adequacy substantially while minimally affecting 40%

60%

80%

100%

120%

140%

160%

180%

200

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uac

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the probability to convert

► The challenge is to analyse the portfolio and understand where price increases could be established to gain margin and fund segments where the uncertainty is greater


-40%

-20%

0%

20%

40%

-

100

200

225 248 273 300 330 363 399 439 483

Pri

ce a

deq

c

Range of prices

price Price adequacy Probabilty of conversion

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► A price increase across the whole portfolio is unlikely to increase the price adequacy efficiently as only the cheapest quotes are accepted

Th t i k i t id tif t t th t t i

The pricing adequacy measure may help to provide a consistent basis to adjust quoted premiums

► The trick is to identify customer segments that can carry a rate increaseFlat increase Use pricing uncertainty

1%

2%

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4%

5%

6%

7%

8%

rob

abil

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den

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fu

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Accept distribution moves to the right but is still on average around 50%

1%

2%

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6%

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8%

rob

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Distribution of ‘accepts’ is now centred around 65%

21

A flat increase will marginally improve the accept distribution of price adequacy

Price changes are made to maximise the pricing adequacy

0%0% 20% 40% 60% 80% 100%

Pr

Pricing adequacy

Distribution of quotes Distribution of accepts


0%0% 20% 40% 60% 80% 100%

Pr

Pricing adequacy


Does pricing uncertainty lead to anti-selection?

► Recall each insurer has a distribution of price points:► In a highly competitive market, such as a price

comparison site, generally only the cheapest (underpriced?) risk is sold

Risk premium calculated by insurer A

Insurer B estimates the risk cost to be less than insurer A.However there is a 45% chance that the actual risk cost is

Ri k i( p )

► This effect is known as the winner’s curse

► Key question is what to do with this information?

Quotes with high pricing 4%

5%

6%

7%

8%

sity

fu

nct

ion

Distribution of pricing adequacy for quotes and accepts

actual risk cost is greater than insurer A’s view.Is Insurer B under pricing?

Potential range of expected risk cost

Risk premium calculated by insurer B

45%

adequacy rarely convert because the quoted premium is uncompetitive in the market place

22

0%

1%

2%

3%

4%

0% 20% 40% 60% 80% 100%

Pro

bab

ility

den

Pricing adequacy



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Which way are you heading?How strong are your prices?

46% 46%34%

80% 60%

66%

Having the information to justify deviances from plan and to spot potential opportunities

Customer segment Target volume

Actual volume Current priceadequacy

Price adequacy to meet target volume

Young drivers 10% 9% 60% 60%

4WD drivers 30% 20% 53% 26%

Over 55s 30% 25% 72% 62%

Urbanites 5% 7% 66% 66%

Commuters 5% 7% 58% 60%

Young couples 20% 32% 45% 57%


Total 100% 100% 57% 50%

► Assume a price adequacy target of 60%

► The “4WD drivers” segment is behind its target volumes but the cost to get to target is too high, if considering the price adequacy

► The “Over 55s” segment volume is also behind target but there is scope to reduce prices and still maintain a healthy price adequacy

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25

30

Conversion model monitoring

Understanding the model’s confidence intervals can indicate when a model needs refreshing

► Confidence intervals can be calculated based on the previously defined

Traditionally we would refresh a demand model

Data the conversion model was built on

0

5

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15

20

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53C

on

ver

sio

n (

%)

Week

Best estimate Lower bound of 95% CI

the previously defined formulae

► Check whether the observation is within the confidence interval► At the 95% confidence

level it is expected that 19

every six months

Best estimate Lower bound of 95% CI

Upper bound of 95% CI Actuallevel, it is expected that 19 out of 20 times, actual observations are within confidence interval

25

The actual experience is outside the CI once in couple of weeks, so the model is still okay

Here the actual experience is consistently outside the CI, so we conclude the model needs to be refreshed


Summary


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Knowing how to use pricing uncertainty is crucial for sustainable growth in a competitive market

► Rate setting for high volume business has to be automated

► However all statistical models have an error term associated

► Understanding customer segments where the error term is uncertain will help to make different pricing decisions


Price setting is not a science, the key is to understand how to blend science and judgment in a cost effective matter

Q&A


Pricing uncertainty: Ignore volatility at your perilThe combination of a dozen or more models could lead to some very uncertain point estimates Pricing uncertainty: Ignore volatility

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