dynamic policyholder behaviour · base level for observed population × factor 1 (based on...
TRANSCRIPT
Dynamic Policyholder BehaviourMatthew Edwards
Chief / Senior Actuaries’ WorkshopWednesday 5 October
06 October 2016
Contents
06 October 2016 2
• Introduction
• Technique
• Examples
• Dynamic relationships
Introduction
06 October 2016
Regulation (Solvency II Delegated Acts)
06 October 2016 4
Article 26 – Policyholder behaviourWhen determining the likelihood that policyholders will exercise contractual options, including lapses and surrenders, insurance and reinsurance undertakings shall conduct an analysis of past policyholder behaviour and a prospective assessment of expected policyholder behaviour. That analysis shall take into account all of the following
a) how beneficial the exercise of the options was and will be to the policyholders under circumstances at the time of exercising the option;
b) the influence of past and future economic conditions;
c) the impact of past and future management actions;
d) any other circumstances that are likely to influence decisions by policyholders on whether to exercise the option.
The likelihood shall only be considered to be independent of the elements referred to in points (a) to (d) where there is empirical evidence to support such an assumption
Regulation (more)
06 October 2016 5
• Article 31 – allow for ‘dependency between two or more causes of uncertainty’
• Article 32 – take into account ‘all factors which may affect the likelihood that policy holders will exercise contractual options or realise the value of financial guarantees.’
• Article 34 – ‘insurance and reinsurance undertakings shall use a method to calculate the best estimate for cash flows which reflects such dependencies.’
Dynamic policyholder behaviour – does it exist?
6
Source: WTW research and annual reports
Financial crisis
Lapse rates for selection of leading life insurers
13 1 3
0% 50% 100%
Type of model used ParametricdistributionTime series
Expert judgement
6 1 3 2
0% 20% 40% 60% 80% 100%
Parametric distributionNormal
Logistic
Lognormal
Other
Willis Towers Watson Risk Calibration Survey 2016
10
1
Primary source of historical data
Internal External
1
3
5
1
Start year of historical data
Pre-1990 1990 - 20002000 - 2005 2006 - 2010
5
2
2
4
10
13
13
11
Separate risk factors to lapse up and down
Expenses stressed under lapse stress
Different stresses for the first and subsequent years
Lapses modelled dynamically under stressed market conditions
Yes No
Do you use the following when modelling lapses?
15 of 17 firms have separate risk factors for lapse and mass lapse
7
Other reasons to model behaviour better
06 October 2016 8
More granular assumption setting of lapse/surrender behaviour can improve• Accuracy of cash flows (unmodelled heterogeneity leads to drift over time)
• Accuracy of pricing assumptions (and minimisation of adverse selection risk)
• Understanding of policyholder behaviour
• Targetting of profitable customers (ie marketing)
Generally ties in with a more ‘customer-centric’ view
Contents
06 October 2016 9
• Introduction
• Technique
• Examples
• Dynamic relationships
EventModelFactors
What is a GLM?
Age
Duration
Benefit size
Lifestyle
Market level
GLM Probability of surrender
© 2016 Willis Towers Watson. All rights reserved. Proprietary and Confidential. For Willis Towers Watson and Willis Towers Watson client use only. 10
GLMs — typical structure
1. What the maths means in practice (example):Probability of surrender in year =Base level for observed population ×Factor 1 (based on duration) ×Factor 2 (based on postcode group) ×Factor 3 (based on amount) ×Factor 4 (based on age) …
2. Each factor is a series of multiplicative coefficients3. All factors are considered simultaneously, allowing
for correlations in the data automatically4. The GLM finds the factor coefficients that will best fit the data5. Method allows for the nature of the random process involved, and provides information about the
(un)certainty of the result6. Robust and transparent — a standard technique for many years in GI, and over five years in life7. For surrender analyses, common to use a different mathematical form (logit transform)
Postcode Group
Multiplier
Group A 0.86
Group B 0.92
Group C 1.00
Group D 1.04
Group E 1.16
© 2016 Willis Towers Watson. All rights reserved. Proprietary and Confidential. For Willis Towers Watson and Willis Towers Watson client use only. 11
Contents
06 October 2016 12
• Introduction
• Technique
• Examples
• Dynamic relationships
Lifestyle (from postcode)
Moneyness of guarantee/option
Other policies
Factors typically found to be predictive Age
GenderPersonal data
Duration
Benefit amount
Options / riders?Policy data
Level of financial market
Bonus historyMarket data
Distribution
Company data
TIME PERIOD FACTOR
(EG CALENDAR YEAR)
13
0
5
10
15
20
0
0.5
1
1.5
2
2.5
3
3.5
Rescaled Predicted Values - Death_Bens
One-way
GLMresults
Effect of death benefit on surrender/lapse (in conjunction with effects of all other factors)
Larger death benefits make policies less likely to surrender, but this effect would not be seen with a normal analysis
14
Effect of Acorn Lifestyle groups on surrender/lapse
0
10
20
30
40
50
60
0.4
0.6
0.8
1
1.2
1.4
A B C D E
Rescaled Predicted Values - New Acorn_Group
15
Incorporating external data
06 October 2016 16
• We can incorporate external data and investigate its usefulness in creating a predictive model
• For instance, we can define a factor based on the difference between the declared fund yield of the insurer in each year and the guarantee attaching to the products
• This example relates to a block of savings business analysed over a 15-year period
• Later, we see how market returns in each year can be used
17
0%
-7%-8%
20%
28%27%26%
18%
-14%
16%
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
fondo-minimo
Log
of m
ultip
lier
0
500000
1000000
1500000
2000000
2500000
<=-0.64% -0.64% 0.86% 0.86% 1.28% 1.28% 1.64% 1.64% 1.86% 1.86% 2.64% 2.64% 3.5% 3.5% 4.57% 4.57% 7.01% >7.01%
Exp
osur
e (y
ears
)
Oneway relativities Approx 95% confidence interval Unsmoothed estimateP value = 0.0%Rank 2/4
Factor based on {yield – guarantee}
Excess of yield over guarantee level
Guarantee bites
Happy policyholders
Grumbly
???
Incorporating external data (2)
Predicting retirement age
Case study The following slides show some indicative results from a recent project investigating the
influence of factors on at-retirement policyholder behaviour Examples of factors found to be predictive: gender, age, policy type, policyholder wealth, time
since last payment to the policy, calendar year (and various others) The influence of financial markets (looked at in terms of equity markets and bond yields) was
borderline predictive Slides are shown with axes / values ‘blued out’
© 2014 Towers Watson. All rights reserved. Proprietary and Confidential. For Towers Watson and Towers Watson client use only.
19towerswatson.com
Age
Rescaled Predicted Values - 19 Age
-200
0
200
400
600
800
1,000
0%
1%
2%
3%
4%
5%
6%
7%
8%
46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
Model Prediction at Base levels
Model Prediction + 2 Standard Errors
Model Prediction - 2 Standard Errors
Comparison against market measures (1)
06 October 2016 21
• GLM results for calendar year compared against a range of plausible market measures
– First graph shows a straight comparison (so an interesting result would be market lines with similar or opposite trend to green GLM line)
– Second graph shows ‘GLM result / market index’ so an interesting result would be a generally horizontal line
• The relationships were also considered allowing for time lags (these showed no difference in predictiveness)
Comparison against market measures (2)
0
2
4
6
8
10
12
14
16
18
0
0.5
1
1.5
2
2.5
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Exposure
Model Prediction at Base levels
ASX Index
FTSE All Share Financials Index
FTSE Actuaries 15y Gilt Yield
Merrill Lynch 15y+ Sterling AA Corporate TRRIndex
Merrill Lynch 15y+ Sterling AA Corporate PRRIndex
Calendar year
0
0.5
1
1.5
2
2.5
3
3.5
4
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
ASX Index
FTSE All Share Financials Index
FTSE Actuaries 15y Gilt Yield
Merrill Lynch 15y+ Sterling AACorporate TRR IndexMerrill Lynch 15y+ Sterling AACorporate PRR Index
Comparison against market measures (3)
Calendar year
Contents
06 October 2016 24
• Introduction
• Technique
• Examples
• Dynamic relationships
25
• An interaction (dependency) relates to how one risk factor varies according to the level of another (different from correlation)
• The ability to model interactions in GLMS can assist in understanding how policyholder behaviour varies with market movements
• The following graph uses the product guarantee * calendar year of exposureinteraction to show how the surrender rate seems to vary according to high or low guarantee levels
• We superimpose a graph of relevant bond yields
Dynamic policyholder behaviour
26
Surrender trends compared with investment market trends
0,0
0,5
1,0
1,5
2,0
2,5
2000 2001 2002 2003 2004 2005 2006 2007
Year
Valu
e of
yie
ld a
nd s
urre
nder
s re
lativ
e to
200
4
1.50-2.5%
4%
Market
Dynamic policyholder behaviour (2)
Calendar year
What does a dynamic policyholder behavior assumption look like?
06 October 2016 27
• From the previous case study / graph:– For low guarantees, market decreases lead to increased surrenders in a fairly linear
manner
– For high guarantees, market decreases seem to lead to decreased surrenders –presumably because policyholders value their guarantees more
• These relationships could reasonably give us the following dynamic adjustments to projected policyholder surrender rates to use in stochastic models:
– for high guarantee products, multiply rates by {yield / 3.6%}
– for low guarantee products, divide by 3 * {yield / 3.6%}
– sensible to add floors/caps to these algorithms (reduced effect beyond the limits)
What does a dynamic policyholder behavior assumption look like? (2)
© 2016 Willis Towers Watson. All rights reserved. Proprietary and Confidential. For Willis Towers Watson and Willis Towers Watson client use only. 28
Triggers level of interest rates profit sharing rates compared to competitors level of equity index financial strength of an insurer
Usage in selected markets (Germany, Austria, France,
Italy) – common market approach for with-profit business
Cap for lapse increases
Floor for lapse decreases
2nd trigger -decrease
1st trigger -decrease
1st trigger - increase 2nd trigger - increase
∆ benchmark vs. technical interest rate
incr
ease
/dec
reas
e in
bas
e la
pse
assu
mpt
ions
06 October 2016 29
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