1. A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK TRONCONI ANDREA Torino, 4 Dicembre 2014 andrea.tronconi@uniroma1.it

2. 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

3. 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 t97% Average Premium t415 € Delta Frequency 101% Delta Average Severity 102% ULR t+1100% Average Premium t+1400 € Average Cost t+1415 € 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

4. Renewal process and New Business not only effect the future premiums level but even frequency and severity. Renewal process Discount trend New Business Tariff structure INTRODUCTION 2/2 4 PREMIUM RISK –SCR CALCULATION BUT…. A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK

5. 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

6. MODEL FEATURES 1/3 6 COLLECTIVE APPROACH DUE TO THE CARD SYSTEM A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK

7. MODEL FEATURES 2/3 7 ATTRITIONAL VS LARGE CLAIMS A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK

8. MODEL FEATURES 3/3 8 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

9. 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

10. 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

11. PROJECTION OF THE PORTFOLIO 2/3 11 EXAMPLE OF PROJECTION A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK

12. PROJECTION OF THE PORTFOLIO 3/3 12 WHERE EXPECTED FREQUENCY A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK

13. 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

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

15. ESTIMATION OF THE FREQUENCY PARAMETER 2/4 15 GRAPH 1 - CAR AGE A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK

16. ESTIMATION OF THE FREQUENCY PARAMETER 3/4 16 GRAPH 2 - AGE A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK

17. ESTIMATION OF THE FREQUENCY PARAMETER 4/4 17 GRAPH 3 - NUMBER OF CLAIMS A PRICING TECHNIQUE TO CALCULATE THE SOLVENCY CAPITAL REQUIREMENT FOR NON-LIFE PREMIUM RISK

18. 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

19. CONCLUSIONS 19 SCR CALCULATION 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

20. 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