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
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE 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….
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
AGENDA
5
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
MODEL FEATURES 1/3
6
amount of a single claim number of claims: FOCUS OF THE PRESENTATION
COLLECTIVE APPROACH
DUE TO THE CARD SYSTEM
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
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
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
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
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
AGENDA
9
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
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?
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
PROJECTION OF THE PORTFOLIO 2/3
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
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
PROJECTION OF THE PORTFOLIO 3/3
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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
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
AGENDA
13
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
ESTIMATION OF THE FREQUENCY PARAMETER 1/4
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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
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
ESTIMATION OF THE FREQUENCY PARAMETER 2/4
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
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A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
ESTIMATION OF THE FREQUENCY PARAMETER 3/4
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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
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A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
ESTIMATION OF THE FREQUENCY PARAMETER 4/4
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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
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A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
AGENDA
18
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
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…
A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK
REFERENCES
20
• 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