INFLATION ADJUSTED CHAIN LADDER METHOD. Bențe Corneliu Cristian 1, Gavriletea Marius Dan 2. Romania

Transcription

1 INFLATION ADJUSTED CHAIN LADDER METHOD Bențe Corneliu Cristian 1, Gavriletea Marius Dan 2 1 The Department of Finance, The Faculty of Economics, University of Oradea, Oradea, Romania 2 The Department of Business, The Faculty of Business, Babes Bolyai University, Cluj- Napoca, Romania cbente@uoradea.ro mgavriletea@yahoo.com Abstract:Claims reserving is one of the basic actuarial tasks in the insurance industry. Based on observed claims development figures (complete or incomplete development triangles or trapezoids) actuaries have to predict the ultimate claim amount for different lines of business as well as for the whole insurance portfolio. In order to fulfil the commitments at any time arising from contracts insurance, insurance companies are required to establish and maintain certain technical reserve. As a result, these technical reserves have a major role in ensuring stability, the financial insurance companies being completely necessary to estimate as correctly. Also the technical background operation is an essential part of insurance companies as related funds are invested and earnings are an important source of income. Calculation of technical provisions is achieved by actuarial methods and their overvaluation or underestimation distorts business of insurers. The overvaluation reserves leads to reduced solvency margin and the company may be unable to make to commitments at a time, and undervaluation influence and profit taxes paid may be higher. The inflation-adjusted Chain-Ladder methodology incorporates an explicit allowance for past and future inflation. This method requires a triangle of paid claims and credible estimates of past and future inflation assumptions. Incremental payments in each calendar period are adjusted by past inflation to the same money terms. This way it assumes that the inflation-adjusted development is stable so that the Chain-Ladder assumption can hold. Then the incremental values are restated again as a cumulative development triangle and the Chain-Ladder method is applied. Finally, as the payments will actually be paid in the future, incremental cash flows will be adjusted by the future inflation assumption to allow for this. All the economic actors active in a market consider and analyse permanently the evolution of the business cycle by using available data in order to make rational choices in their business decision. In other words, the decision making relies in all its phases and in all circumstances on data, here including statistical data. It is important for an insurance company that, through its programming for how they will achieve security, aware of the risks that may arise for them commensurable, ie probabilistic estimate them, so things will market the normally. In this way, for damage or for those that are outstanding or unreported or random propose a methodology based on which one who engages in this way to know what to do. Key words: claims reserving, chain-ladder method, damages, premium rates. JEL Classification: G22 1. Introduction 370

2 Based on the probability theory is an attempt to investigate indeterminacy, insurance companies must calculate insurance premiums so as to cover all operating expenses and achieve anticipated profit, preserving the principle of equity and solidarity. With this in dealing with the insurance company actuary, using various actuarial statistical methods. Actuary knowledge in finance and risk management are fully utilized in insurance. Actuaries have a decisive role in the design, pricing and product evaluation. The actuaries have a key role in decision making in the management of insurance companies and pension funds. Knowledge conduct commercial insurance business requires measurement, structuring and aggregation phenomena and processes in insurance, taking place in the insurance market. Depending on the subject phenomenological research, statistics as a scientific discipline and practice of social-economic tool, separate the fields in which insurance actuarial analysis plays an almost unknown, while the insurance share in the national economy maintained an upward trend. Actuarial analysis contributes to decision making in an insurance company because they are determined based on the size and value risk (risk premium), which is considered an essential element of both life insurance and general insurance. The professionalism in determining the risk depends mostly insurer's financial result. In business insurance plays a particularly statistical research on estimation of insurance business and prospects of achieving them. To this end, the events taking place in insurance are measured, orderly, systematic and aggregated by observation (collection), processing and analysis. 2.Claims Reserving With Inflation Adjusted Chain Ladder Method Chain ladder reserving methods have been discussed in the actuarial literature for many years. Taylor (1986) dates the al methodology back to Harnek (1966). Taylor, describes chain ladder models for reserving as those that chain a sequence of ratios together into a ladder of factors... which enable one to climb from experience recorded to date to its predicted ultimate value (Taylor,2000). Taylor provides a detailed overview of traditional chain ladder reserving methods, as does Booth, Chadburn, Cooper, Haberman, and James (Booth et al., 1999). Current techniques can be applied to so-called run-off triangles containing either paid losses or incurred losses (for example, the sum of paid losses and case reserves). In a run-off triangle, observable variables are summarized by arrival (or ) year and development year combination. An arrival year is the year in which the claim occurred, while the development year refers to the delay in payment relative to the arrival year (Bente&Bente, 2011). The most popular approach is the chain ladder approach, largely because of its practicality. However, the use of aggregate data in combination with (stochastic variants of) the chain ladder approach (or similar techniques) gives rise to several issues. Chain Ladder method involves taking inflation into account inflation index applied to damage from previous years and projected rate applied to estimate damages. The basic Chain Ladder Method apply data on damages updated inflation index to estimate the damages to be paid in subsequent years, after applying the index forecasted to convert that amount into monetary values for each year. Therefore, this method differs 371

3 from the basic one by the fact that the data are expressed in terms of current, while in the method using the data base in real terms. Damages paid for accumulating insurance company taken as an example are presented in the following table development (data are expressed in thousand euros). Table 1: Incremental Paid Claims , , , , , , , , , , , , , , ,000 The annual inflation rate in the middle of each year in the period under review were: Table 2: Annual inflation rate Year Inflation ,09 % ,79 % ,33 % ,98 % Source: This model requires the following steps to find the reserve for outstanding claims taking into account inflation. The first stage inflation matrix calculated above, starting from the previous inflation. Table 3: Inflation matrix ,0609 0,0579 0,0333 0,0398 0,00 1,0609 1,0579 1,0333 1,0398 1,00 1,2058 1,1366 1,0744 1,0398 1,00 372

4 The cells were calculated as follows: 1,2058 = 1,0609 x 1,0579 x 1,0333 x 1,0398 1,1366= 1,0579 x 1,0333 x 1,0398 1,0744 = 1,0333 x 1,0398 Table of development for inflation is shown below: Table 4: Table of development ,2058 1,1366 1,0744 1,0398 1, ,1366 1,0744 1,0398 1, ,0744 1,0398 1, ,0398 1, ,00 Damage adjusted by inflation is calculated by multiplying the data cell by cell development in tables containing initial damage and inflation. Obtained new table containing the damage expressed in current prices. Table 5: Table of development Further, it is applying the Basic Chain Ladder Method, with the last input data table development. This cumulative damage to yield development following table: Table 6: Table of development 373

5 We are calculating the development factors for each period: r 0,1 = = 1,7195 r 1,2 = = 1,2111 r 2,3 = 1,0937 r 3,4 = = 1,0515 We are estimating the unliquidated cumulative damage using growth factors calculated previously. Table 7: Table of development , , , , , , , , , ,3857 For 2014: C2014,1 = x r 0,1 = x 1,7195 = ,871 C2014,2 = x r 0,1 x r 1,2 = x 1,7195 x 1,2111 = ,5416 C2014,3 = x r 0,1 x r 1,2 x r 2,3 = x 1,7195 x 1,2111 x 1,0937 = ,6160 C2014,4 = x r 0,1 x r 1,2 x r 2,3 x r 3,4 = x 1,7195 x 1,2111 x 1,0937 x 1,0515 = ,3857 For 2013: C2013,2 = x r 1,2 = x 1,2111 = ,4397 C2013,3 = x r 1,2 x r 2,3 = x 1,2111 x 1,0937 = ,1365 C2013,4 = x r 1,2 x r 2,3 x r 3,4 = x 1,2111 x 1,0937 x 1,0515 = 374

6 18.701,0711 For 2012: C2012,3 = x r 2,3 = x 1,0937 = ,2143 For 2011: C2011,4 = x r 3,4 = x 1,0515 =16.266,705 To determine the estimated damage simple values, are subtracted from the cumulative damage the table above, column by column, and then obtain: Table 8: Table of development , , , , , , , , , ,7697 Inflation in the analysed period is between 3.33% and 6.09%, and the forecast for the period , in the middle of each year is shown below: Table 9: Table of development ,03 0,04 0,05 0,05 1 1,03 1,04 1,05 1,05 1 1,030 1,0712 1,1247 1,1809 The data in this table were obtained as follows: = 1.03 x = 1.03 x 1.04 x = 1.03 x 1.04 x 1.05 x 1.05 Table of development for future inflation builds on data: 375

7 Table 10: Table of development , ,00 1, ,00 1,030 1, ,00 1,030 1,0712 1, ,00 1,030 1,0712 1,1247 1,1809 We are adjust the accumulating damage to future inflation by multiplying the data cell by cell, development of tables for future inflation and expected damage in simple values: Table 11: Table of development , , , , , , , , , ,2249 Source: Processed by author Based on the table above is determined by summing the cumulative damage data column by column. Table 12: Table of development , , , , , ,

8 , , , ,9415 The reserve for unliquidated claims at is: RDN = (26.316, ) + (19.008, ) + (21.793, ) +(16.290, ) = ,1952 RDN = ,1952 The unliquidated damage estimated to pay during the period can be calculated from the penultimate development table: 2015 = , = 6.881, = 3.351, = 1.465,2249 Adding outstanding damage during , we obtain reserve for outstanding claims NDR = This value is reflected in the balance sheet of the company. 3. Conclusions Actuarial analysis contributes to decision making in an insurance company because they are determined based on the size and value risk (risk premium), which is considered an essential element of both life insurance and general insurance. The professionalism in determining the risk depends mostly insurer's financial result. In business insurance plays a particularly statistical research on estimation of insurance business and prospects of achieving them. To this end, the events taking place in insurance are measured, orderly, systematic and aggregated by observation (collection), processing and analysis. Risk estimation and obligations of the insurer on the basis of inadequate or inaccurate data is an extremely dangerous situation. Therefore, the insurer is extremely important to establish the best possible observation and use of data. Data processing by determining risk and compliance, with a special role to characterize the state insurance business and to assess economic performance must be based on a proper filing system correspondingly able to provide reliable data on the one hand and, on the other hand, to be based on a concept and methodology to enable the ordering, structuring and aggregation of data by scientific principles. Therefore, observation, collection and recording of information are key elements in the business insurance actuarial estimates. Background premium rates and reserves is an important activity for insurance companies. If insurers do not establish premium rates that accurately reflect the size of the risk they may incur losses due to financial imbalance created between raw or damages due to adverse selection. I also believe that insurance companies who do not substantiate scientifically premium rates and adapts them those of other insurers in the market are made in the face of danger have a small volume of insurance premiums too high or because a large resulting in loss insurance since premiums are too small. Technical substantiation must be based on specific methods because of the possibility that insurers use two different calculation techniques for similar obligations and get completely different results thus disturbing profitability and financial strength. Sometimes true values of the records though not real financial picture illustrates the insurer reserves the right to not substantiate the due. The Chain Ladder method predicts the right total reserve if the payment is multiplicative in 377

9 the occurrence year dimension. It predicts the right reserve of known claims if the payment is multiplicative in the run-off after reporting time dimension. Therefore it is a matter of structure or symmetry of the claim payments if the Chain Ladder method is an appropriate estimation method for the reserves or not. These arguments concerning the structure of the claim payments are of course also valid for the claim numbers. Therefore Chain Ladder estimates of claim numbers are biased, if the data structure does not have the right form. This is of importance because in practice Chain Ladder estimates of the ultimate claim numbers are sometimes used for IBNR calculation It is noted that if the analysed company reserves were based rigorously taking into account inflation. Setting up a reserve for damage inadequate outstanding imbalances could lead to the insurer by distributing dividends unfounded because it influences the size of the profit, and your company to make losses in reality. However, the insurer may seem creditworthy, but solvency is also based on improper establishment of reserves for outstanding damage. References: Armeanu, D. (2005), Risk and uncertainty in insurance, Cison Publishing, Bucharest, Benţe C., Benţe F.M.(2011), "Valuation and Reserving Technique in the General Insurance", in the book "Contemporary Legal and Economic Isues III", Osijek Booth, P., R. Chadburn, D. Cooper, S. Haberman, and D. James (1999), Modern Actuarial Theory and Practice, Chapman & Hall/CRC Press LLC, New York Bowers, N.L., jr., Gerber, H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J. (2000). Actuarial Mathematics, The Society of Actuaries, Schaumburg, Illinois Cairns, A.J.G. (2000), A Discussion of Parameter and Model Uncertainty in Insurance, Insurance: Mathematics and Economics 27 (3), pp De Alba, E. (2002), Bayesian Estimation of Outstanding Claim Reserves, North American Actuarial Journal 6 (4), pp England, P., and R.J. Verrall. (2002), Stochastic Claims Reserving in General Insurance, Sessional Meeting Paper Presented to the Institute of Actuaries on January 28 Kremer, E.. (1982), IBNR-Claims and the Two-Way Model of ANOVA, Scandinavian Actuarial Journal 1, pp Lamps, D. (2002), Bayesian Analysis of Claim Lag Data Using WinBUGS Software. Presented at the Annual Meeting of the Society of Actuaries, Boston, Massachusetts, October Ntzoufras, I., and P. Dellaportas. (2002). Bayesian Modeling of Outstanding Liabilities Incorporating Claim Count Uncertainty, North American Actuarial Journal 6, pp Rosenberg, M.A., and V.R. Young (1999), A Bayesian Approach to Understanding Time Series Data, North American Actuarial Journal 3 (2), pp Scollnik, D.P.M. (2001), Actuarial Modeling with MCMC and BUGS, North American Actuarial Journal 5 (2), pp Taylor, G.C. (2000), Loss Reserving: An Actuarial Perspective, Kluwer Academic Publishers, Norwell 378

10 Verrall, R.J. (1989), A State Space Representation of the Chain Ladder Linear Model, Journal of the Institute of Actuaries 116, pp Verrall, R.J. (1990), Bayes and Empirical Bayes Estimation for the Chain Ladder Model, ASTIN Bulletin 20,, pp