Demand and Price Elasticity Modelling · 24/11/2015 1 Demand and Price Elasticity Modelling Dr. Ji Yao a,b The views and opinions expressed in this presentation are independent of

24/11/2015

1

Demand and Price Elasticity Modelling

Dr. Ji Yao a,b

The views and opinions expressed in this presentation are independent of employer of

the presenter or the Actuarial Profession

a. RPC Consulting b. University of Kent

Agenda

• Introduction

• Current approaches used in the market

• Common pitfalls and considerations of

the GLM approach

• Decision tree type approach

• Summary and Q & A

24/11/2015

2

Colour palette for PowerPoint presentations

Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184

Secondary colour palette

Primary colour palette

Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

November 24, 2015 3

Introduction

• The idea initiated by a CAS call for monograph in early 2015

• Purpose of this research

– Survey of different methods of conversion and elasticity models

– Research on new methods

– Not limited to insurance industry

3


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

November 24, 2015 4

What is demand model

• Demand is defined as the number of sales divided by number of

quotes/renewal invites

• Conventionally called ‘conversion model’ for new business and

‘retention model’ for renewal business

• Premium might or might not be a factor in the model

4

24/11/2015

3


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

November 24, 2015 5

What is price elasticity model

•Price elasticity measures the change in demand divided by the change

in premium, mathematically,

•Conventionally add the minus sign to make it a positive number

5


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

Demand and price

elasticity model

Demand and price elasticity models are

important components in pricing analysis

6 Page 6

Risk cost /

expense

model

Quote

Pool

Conversion

model

Retention

model

Pricing

scenarios

Ageing

Models

In-

force

Pool

Total profit

Expected

profit per

quote

Iterate until

achieve

business

objective

• Price elasticity model is particularly important in price optimisation

24/11/2015

4


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72 Agenda

• Introduction



the GLM approach




Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

November 24, 2015 8

Current approaches used in the market

• One-way and two-way analysis

• Easy to calculate

• Ignore correlation in the explanatory variables

• Not suitable for complicated analysis

• Generalised linear model (GLM)

• Generalised non-linear model

• Guarantee that elasticity is always positive

• Computationally intensive

• Neural networks

• Understand the results is a challenge

24/11/2015

5


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

November 24, 2015 9

The GLM approach: price elasticity derived

from the demand model

Model setting

• Logit link function

• Binomial distribution error structure

• Linear component

d

not p


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

November 24, 2015 10

It is important to have randomised price tests

• GLM explains the difference in demand by normal rating

factors (age, area etc) and premium

• If the price test correlated with one rating factors, GLM will

get confused whether it is the rating factor or the price

difference cause the difference in demand

Age Demand

Young 10%

Old 20%

Age Demand -

Champion

Demand -

Challenge

Young 10% 20%

Old 20% 25%

Age Demand -

Champion

Demand –

Challenge

Young 20%

Old 20%

Base scenario Random price test

Extreme scenario: Young always gets discount

24/11/2015

6


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72 Agenda

• Introduction



the GLM approach




Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


Price elasticity can only be observed for a

group of risk

• Reconciliation of price elasticity at individual level is always

an approximation

Infinite elasticity

at £500

Infinite elasticity

at £450

24/11/2015

7


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


Non-linearity or break point are expected in

demand model

• Demand depends on the market premium and own premium

• Even simple pricing action can give non-linearity effect in

demand


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72



demand model



demand

24/11/2015

8


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72



demand model



demand


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

November 24, 2015

• Where there is limited number of sales, the model largely

depend on extrapolation of neighbouring segments

16

Extrapolate of model is common but much

more dangerous

Demand in high

mileage relying on

the mid-range

mileage. It can't tell

the difference in

elasticity.

24/11/2015

9


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


Derived elasticity has high uncertainty

17

Elas = (15%-10%)/10%/5% = 10 If SD of conv is 10% of conv,

SD of Elas is

(1%^2+1.5%^2)^0.5/10%/5% = 3.6,

36% of Elas

• Uncertainty of price elasticity is compounded by uncertinty

of demand

• And dominated by the high uncertaint point


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


Model reconciliation

• One way chart

18

•How to calculate actual price

elasticy? Is it possible?

•How to calculate modelled

price elasticity?

•How to make them

consistent and comparable?

24/11/2015

10


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


Model reconciliation

• Lift curve is even more a challenge

19

•How to calculate model price

elasticity for individual

policy? What is the price

point?

•Calculate model and actual

price elasticity in bands is

same as one way chart


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


Understand the impact of model uncertainty

20

Risk cost /

expense

model

Conversion

model

Retention

model

Expected

profit per

quote

Optimal

premium

• This uncertainty is compounded with winner's curse

24/11/2015

11


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72 Agenda

• Introduction



the GLM approach




Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


Decision tree

22

24/11/2015

12


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


Idea of tree based approach

• Decision tree appraoch provides a top-down approach that focus on

segments

23

Champion Challenge

Elasticity = 5

Champion Challenge

Champion Challenge

Elasticity = 7

Elasticity = 3

• Split at a place that differentiate the price elasticity most


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


The idea of tree based approach

24

Champion Challeng

e

Champion Challenge

Elasticity = 7

Elasticity = 4

Cha

mpio

n

Chal

leng

e

Elasticity = 2

24/11/2015

13


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


GLM could be applied to adjust the difference in

mixture

• Algorithm

– Step 1: For each possible split, build a GLM on demand including price test as

a explanatory vairable. Record the impact of price test.

– Step 2: Find the split that has the maximum impact of price test

– Step 3: If stop criteria is not met, go to Step 1. Otherwise, stop.

– Step 4: Build GLM in each leaf of the tree

25


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

November 24, 2015

Literatures

•Using Generalised Linear Model to Build Dynamic Pricing Systems, Karl P.

Murphy, Michael J. Brockman, and Peter K. W. Lee

•Beyond the Cost Model: Understanding Price Elasticity and Its Applications,

Serhat Guven, FCAS, MAAA, and Michael McPhail, FCAS, MAAA

•Real-World Uplift Modelling with Significance-Based Uplift Trees, Nicholas J.

Radcliffe

•An Application of Genetic Algorithms to Uplift Modelling, David P. Hofmeyr

•Optimal personalized treatment rules for marketing interventions: A review of

methods, a new proposal, and an insurance case study, Leo Guelman,

Montserrat Guillén and Ana M. Pérez-Marín

•Demand Modelling Working Party report, James Tanser, John Light, Sophia

Mealy and Owen Morris

26

24/11/2015

14


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72

November 24, 2015

Summary

•Demand and price elasticity models could be spuriously accurate

•Great attention is needed in model check and understanding

uncertainty

•Decision tree type model is a top-down approach that focus on

segments, that potentially reduce spurious accuracy

27


Dark blue

R17 G52 B88

Gold

R217 G171 B22

Mid blue

R64 G150 B184



Light grey

R63 G69 B72

Pea green

R121 G163 B42

Forest green

R0 G132 B82

Bottle green

R17 G179 B162

Cyan

R0 G156 B200

Light blue

R124 G179 B225

Violet

R128 G118 B207

Purple

R143 G70 B147

Fuscia

R233 G69 B140

Red

R200 G30 B69

Orange

R238 G116 29

Dark grey

R63 G69 B72


Expressions of individual views by members of the Institute and Faculty of

Actuaries and its staff are encouraged.

The views expressed in this presentation are those of the presenter.

Questions Comments

Documents

Demand and Price Elasticity Modelling · 24/11/2015 1 Demand and Price Elasticity Modelling Dr. Ji Yao a,b The views and opinions expressed in this presentation are independent of