a pricing technique to calculate the solvency capital requirement for non-life premium risk tronconi...

A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT

FOR NON-LIFE PREMIUM RISK

TRONCONI ANDREATorino, 4 Dicembre 2014

andrea.tronconi@uniroma

1.it

AGENDA

2

INTRODUCTION

MODEL FEATURES

PROJECTION OF THE PORTFOLIO

ESTIMATION OF THE FREQUENCY PARAMETER

CONCLUSIONS

A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK

Delta Frequency;

Delta Average Severity;

Average Premium.

INTRODUCTION 1/2

3

The Premium Risk derives from fluctuations in timing of frequency and severity, of insured events, which ensure that the premiums income will be not enough to pay future claims.In this context the perception is a lack of connection with actuarial best practices of pricing.

ULR t 97%

Average Premium t 415 €

Delta Frequency 101%

Delta Average Severity 102%

ULR t+1 100%

Average Premium t+1 400 €

Average Cost t+1 415 €

Delta -3,5%

RISK AREAS

PROJECTION OF INCOME & COST

PREMIUM RISK


Renewal process and New Business not only effect the future premiums level but even frequency and severity.

Renewal processDiscount trendNew BusinessTariff structure

INTRODUCTION 2/2

4

• distribution of the total claim amount•Simulating approach to derive the probability distribution of •Instead of we will use , which is an estimation of the next year premiums income

PREMIUM RISK –SCR CALCULATION FACTORS CONNECTED WITH

BUT….


AGENDA

5

INTRODUCTION

MODEL FEATURES



CONCLUSIONS


MODEL FEATURES 1/3

6

amount of a single claim number of claims: FOCUS OF THE PRESENTATION

COLLECTIVE APPROACH

DUE TO THE CARD SYSTEM


MODEL FEATURES 2/3

7

For each claim types we will consider a new segmentation (attritional / large). Focusing on the NC claims:

Being the treshold between large and attritional :

ATTRITIONAL VS LARGE CLAIMS


MODEL FEATURES 3/3

8

is an external parameter which considers a market change in the overall frequency of NC claims.How to derive the future expected level of ?

FREQUENCY

Policies that have at least one day of coverage during the solvency period considered (the level of expected frequency is connected to the features of the policies in portfolio)

Multivariated models that explain the frequency (built and used by the actuarial department to construct the tariff)

STARTING POINTS


AGENDA

9

INTRODUCTION

MODEL FEATURES



CONCLUSIONS


PROJECTION OF THE PORTFOLIO 1/3

10

Renewal process Company probability of renew (maybe depending on the agency)

New business Connection with the business plan: is the company going to open some

agencies somewhere? How many new business policies are expected?

Assumption: the features of the new business policy are equal to the ones of the last year new business policies

Future tariff

Discount trend

WHAT SHOULD BE CONSIDERED?



11

EXAMPLE OF PROJECTION

Jan Feb Mar Apr May Jun Jul Ago Sep Oct Nov Dec

Age Car Type λNC Age Car Type λNC

27 Audi A3 5% 28 Audi A3 4.5%

Age Car Type λNC Age Car Type λNC50 VW Golf 1.5% 51 VW Golf 1.7%

Age Car Type λNC18 VW UP 7%

Age Car Type λNC

33 BMW S1 5%

TIMELINE

POLICY 1

POLICY 2

POLICY 3 NB

POLICY 4



12

WHERE

Policy Exposure A λNC,A Exposure P λNC,P n NC,YEAR

1 3/12 5% 9/12 4.50% 4.63%2 8/12 1.50% 4/12 1.70% 1.57%3 "Missing" "Missing" 9/12 7% 5.25%4 5/12 5% "Missing" "Missing" 2.08%

Having the frequency ante and post renew we can calculate, for each profile, the expected frequency of the year and then the of the whole portfolio:

EXPECTED FREQUENCY


AGENDA

13

INTRODUCTION

MODEL FEATURES



CONCLUSIONS


ESTIMATION OF THE FREQUENCY PARAMETER 1/4

14

FOR POLICY N.1 WE HAVE THAT

We use the pricing multivariate model that explain the NC frequency .

HOW TO CALCULATE ?

GLM models are the best practice in the tariff process cause take in account correlations between variables.In the following slides there are some interesting results

GLM

Jan Feb Mar Apr May Jun Jul Ago Sep Oct Nov Dec

Age Car Type λNC Age Car Type λNC

27 Audi A3 5% 28 Audi A3 4.5%

TIMELINE

POLICY 1



15

GRAPH 1 - CAR AGE

0 5 10 15 20 25 300.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Car Age

Re

lati

vit

ies



16

GRAPH 2 - AGE

10 20 30 40 50 60 70 80 90 100 1100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Age of the policy holder

Re

lati

vit

ies



17

GRAPH 3 - NUMBER OF CLAIMS

0 2 4 6 8 10 12 14 16 180

0.5

1

1.5

2

2.5

3

Number of Claims

Re

lati

vit

ies


AGENDA

18

INTRODUCTION

MODEL FEATURES



CONCLUSIONS


CONCLUSIONS

19

Replicating this approach for each claim types we calculate the frequency parameters that we need to start the simulations, and finally we reach the distribution of .This process allows to calculate the percentile of and the SCR.

SCR CALCULATION

Includes the CARD System Considers the real risk profile of the

company Takes into account the Company

strategies Is strictly connected to actuarial pricing

technique Considers future tariff and the discount

trend in the calculation of Can easily include reinsurance

structures

MAIN FEATURES

All of these aspects helps the Company Board to take decisions, answering to the following fundamental question: “What will happen in terms of expected profitability, loss ratio, SCR, size of portfolio if ….?”

WHAT IF…


REFERENCES

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• C.D. Daykin, T. Pentikainen, M. Pesonen, “Practical Risk Theory for

Actuaries”, 1993;

• ANIA, “CARD, convenzione tra assicuratori per il risarcimento Diretto”,

2013;

• Towers Watson, “Practitioner’s Guide to Generalized Linear

Models”,2004;

• EIOPA, “QIS5 Technical Specifications”,2010;

• FINMA, “Technical Document on the Swiss Solvency Test”, 2007;

• Swiss Federal Office of Private Insurance, “White Paper of the Swiss

Solvency Test”, 2004.


a pricing technique to calculate the solvency capital requirement for non-life premium risk tronconi...

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