Solvency Testing Model SDCNSF

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Solvency Testing Model SD-CNSF

• México

October, 2002
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Contents

• Background
• Solvency Testing Model
• Dynamic Solvency System
• Perspectives

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Background
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Background

• In Mexico, the insurance operations are carry out
  under a dynamic behavior of financial and risk
  variables. This situation occurs mainly because a
  business line high rotation, competition and
  inflation effects. At the same time, traditional
  insurance companies are not specialized and they
  can manage both, life insurance and non-life
  insurance, increasing the administration
  complexity.

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Background

• For this reason it is important to have efficient
  risk analysis tools, for identifying business
  line risk factors and analyzing capital
  sufficiency in the medium and short term.

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Background

• The National Insurance and Surety Commission of
  Mexico (CNSF) has been developing a Dynamic
  Solvency Testing Model to encourage
  self-regulatory practices by insurance
  enterprises, and at the same time strengthen
  preventive supervision.
• Based upon the mathematical analysis solvency
  model, a dynamic solvency testing computing
  system (SD-CNSF) was developed, which allows a
  prospective analysis of both solvency and risk
  exposure factors.

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Solvency Testing Model
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Solvency Testing Model

• The dynamic solvency model of the CNSF
  incorporates aspects of the Mexican regulation,
  as well as the laws of the behavior of the risk
  variables of each insurance line of business in
  Mexico.

• Probability density functions have been fitted
  using the last five years statistical information
  from the Mexican market.

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Solvency Testing Model

• The statistical data correspond to each companys
  claim amount for a specific business line i,
  MRi(t). The claims amount is expressed as a
  percentage of the written premium PEi(t), loss
  ratio. The loss ratio t for business line i at
  year t is expressed as

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Solvency Testing Model

• For each insurance business line, it was proved
  through statistical analysis, that the loss ratio
  random variable, has the typical characteristics
  of a gamma probability function, whose
  mathematical expression is

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Solvency Testing Model

• Consequently, gamma density functions were
  fitted, for each business line, using Mexican
  insurance companies statistical data.

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Solvency Testing Model

• A Kolmogorov-Smirnov goodness-of-fit test was
  performed to prove the probability distribution
  functions adequacy on each business line. The
  Kolmogorov-Smirnov goodness-of-fit test is based
  on the absolute value of the maximum difference
  between the sample cumulative distribution values
  and the hypothetical cumulative distribution

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Solvency Testing Model

• The probability density functions for each
  business line are as shown

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Solvency Testing Model

• The companys capital position at time t (CAPt),
  can be expressed as the companys capital
  position at time t-1 (CAPt-1) plus the capital
  contributions at time t (ACt) plus the operation
  flow (profit or loss) at time t (Rt)

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Solvency Testing Model

• The insurance companys solvency margin at time
  t, is calculated as a portion of companys
  assets at time t (g), minus the solvency
  requirement at time t

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Solvency Testing Model

• The companys solvency requirement (RS(t)) is
  obtained by adding the solvency requirements of
  every business line

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Solvency Testing Model

• The operational flow of the insurance company at
  time t, is calculated as the difference between
  inflow (premium, investment earnings) and outflow
  (expenses, premium reserves, ceded premium,
  claims) at time

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Solvency Testing Model

• Written premium (PE), is simulated based on the
  historic premium growth rate of the company in
  the last five years, for each business line,
  making the growth rate fluctuate, within a small
  interval of values around the historic by using
  a uniform distribution function

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Solvency Testing Model

• Retention Premium (PR) is calculated by
  multiplying a historic rate of retention
  premium, by the written premium, making the rate
  of retention premium fluctuate, within a small
  interval of values around the historic value by
  using a uniform distribution function.

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Solvency Testing Model

• Acquisition Cost (CA) is calculated as a
  percentaje of the retention premium (historical
  percentage), making the percentage fluctuate,
  within a small interval of values around the
  historical value by using a uniform distribution
  function

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Solvency Testing Model

• Administrative Cost (CO) is calculated with a
  formula that involves a part as fixed cost, and
  another part as variable cost that depends on the
  premium

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Solvency Testing Model

• Investement Earnings (PF), is calculated as the
  amount of assets multyplied by their asset yield
  rates, making each rate fluctuate, within a small
  interval of random values in accordance with the
  expected trend

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Solvency Testing Model

• Premium reserve is calculated, in the case of
  short term insurance, as a percentage of the
  retention premium. The portion of unearned
  premium reserve is calculated by a formula which
  involves the average retention premium of last
  two years

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Solvency Testing Model

• The simulation process, is based on the so-called
  inversion method, which consists in generating
  random numbers with a continuous uniform
  distribution on (0,1), and then applying the
  inverse of the cumulative distribution function
  of the loss ratio random variable

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Solvency Testing Model

• Finally, with the model it is possible to
  generate several scenarios and calculate a ruin
  probability as well as the expected value of
  future capital necessities.

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• Dynamic Solvency System

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Dynamic Solvency System

• Based on the dynamic solvency model, the CNSF has
  developed a dynamic solvency computing system
  (SD-CNSF), which carries out simulations of
  stochastic processes based on each of the
  insurance business lines probability functions,
  as well as on the companys business plan
  scenarios.
• The input information of the system is a data
  base, which contains all financial information of
  the company in the last five year.

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Dynamic Solvency System

• The system functioning is based on the
  information, processes and the next results

Financial Statementes
Estimated Risk Factors
Business Plan
Projected Financial Statements
Invested Assets
Future Capital Necessities
Macroeconomical Expectations

• Processes
• Stochastic Proceeses
• Simulations
• Scenarios
• Index Calculatios
• Grafhs

Risk Probability Functions
Sensitivity Analysis Results
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Dynamic Solvency System

• Next, we are going to show the Dynamic Solvency
  Computing System (SD-CNSF).

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Perspectives
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Perspectives

• The development of the Dynamic Solvency Computing
  System (SD-CNSF), is in an initial phase. We hope
  to improve and to incorporate new routines in
  order to increase its efficiency.
• The Dynamic Solvency Computing System (SD-CNSF),
  will allow to implement preventive regulation.
• The Dynamic Solvency Computing System (SD-CNSF),
  is a quite flexible tool that could be updated to
  the normative changes.

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Solvency Testing Model SD-CNSF

• October, 2002