Demand and Price Elasticity Modelling

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

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 of Kent

b. University

Agenda • Introduction • Current approaches used in the market • Common pitfalls and considerations of the GLM approach • Decision tree type approach • Summary and Q & A

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Introduction • The idea initiated by a CAS call for monograph in early 2015 • Purpose of this research

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– Survey of different methods of conversion and elasticity models – Research on new methods – Not limited to insurance industry

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What is demand model

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• 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

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What is price elasticity model •Price elasticity measures the change in demand divided by the change in premium, mathematically,

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

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Demand and price elasticity models are important components in pricing analysis

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Risk cost / expense model

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Quote Pool

Pricing scenarios

Conversion model

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Inforce Pool

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Retention model

Ageing Models

Demand and price elasticity model Iterate until achieve business objective

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Expected profit per quote

Total profit

• Price elasticity model is particularly important in price optimisation

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Agenda • Introduction • Current approaches used in the market • Common pitfalls and considerations of the GLM approach • Decision tree type approach • Summary and Q & A

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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

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The GLM approach: price elasticity derived from the demand model Model setting

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d



Logit link function



Binomial distribution error structure



Linear component

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not p

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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 Random price test

Base scenario Age

Demand

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Young

10%

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20%

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Age

Demand Champion

Demand Challenge

Young

10%

20%

Old

20%

25%

Extreme scenario: Young always gets discount

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Age

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Young

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Old

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Demand Champion

Demand – Challenge 20%

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Agenda • Introduction • Current approaches used in the market • Common pitfalls and considerations of the GLM approach • Decision tree type approach • Summary and Q & A

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Price elasticity can only be observed for a group of risk

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Infinite elasticity at £500

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Infinite elasticity at £450

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Reconciliation of price elasticity at individual level is always an approximation

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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

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palette for PowerPoint presentations colour palette

Dark blue R17 G52 B88

Gold R217 G171 B22

Mid blue R64 G150 B184

Light 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

ary colour palette

Dark 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

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palette for PowerPoint presentations colour palette

Dark blue R17 G52 B88

Gold R217 G171 B22

Mid blue R64 G150 B184

Light 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

ary colour palette

Dark 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

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Extrapolate of model is common but much more dangerous •

Where there is limited number of sales, the model largely depend on extrapolation of neighbouring segments

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Demand in high mileage relying on the mid-range mileage. It can't tell the difference in elasticity.

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Derived elasticity has high uncertainty

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Elas = (15%-10%)/10%/5% = 10

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• •

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

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Model reconciliation • One way chart

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•How to calculate actual price elasticy? Is it possible? •How to calculate modelled price elasticity? •How to make them consistent and comparable?

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Model reconciliation • Lift curve is even more a challenge

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•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

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Understand the impact of model uncertainty Risk cost / expense model

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Conversion model

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Expected profit per quote

Optimal premium

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Retention model

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This uncertainty is compounded with winner's curse

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Agenda • Introduction • Current approaches used in the market • Common pitfalls and considerations of the GLM approach • Decision tree type approach • Summary and Q & A

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Decision tree

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Idea of tree based approach

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• Decision tree appraoch provides a top-down approach that focus on segments Elasticity = 3

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Champion

Champion

Challenge

Champion

Challenge

Challenge

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Elasticity = 5

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Elasticity = 7

• Split at a place that differentiate the price elasticity most

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The idea of tree based approach

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Elasticity = 4

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Elasticity = 2

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Champion

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Cha mpio n

Challeng e

Chal leng e

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Champion

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Challenge

Elasticity = 7

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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

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Literatures

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•Using Generalised Linear Model to Build Dynamic Pricing Systems, Karl P. Murphy, Michael J. Brockman, and Peter K. W. Lee

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•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

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Summary

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•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

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Questions

Comments

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Expressions of individual views by members of the Institute and Faculty of Actuaries and its staff are encouraged.

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

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