Insurers demand for reinsurance

1
Insurers demand for reinsurance

• Lecture 7 - Economics of insurance
• EOCN6053 Selected topic in financial economics
• Raymond Yeung, PhD
• Honorary Assistant Professor
• 12 April 2007

2
Background

• Reinsurers provide risk capital to direct
  insurers as we have seen in the option pricing
  model
• However, reinsurance takes the form of not only
  excess loss cover (XL) but also quota share (QS)
  for 100 dollar direct premiums written by
  primary insurers a of business is ceded to
  reinsurers
• This reflects that primary insurers are not
  simply purchasing a risk cover from reinsurers
  but also obtaining financial capital from other
  firms
• If open capital market is available, why do
  specialised reinsurers exist?

3
Two explanations for reinsurers

• There are two possible explanations. The first
  one (Borch 1962) is that risk averse primary
  insurers simply seek another risk sharing entity.
  But it is difficult to explain why insurance
  companies, like many other financial
  institutions, are risk averse. We have long
  assumed that insurers are risk neutral
• Latest advancement in financial economics offer
  another theory a layer of financial
  intermediaries exist because they possess
  expertise and knowledge that is surperior than
  open market investors. These intermediaries can
  tackle moral hazard of primary insurers

4
Three-party models

• Primary layer entities engaging in risky
  project, but is able to affect the probability of
  success. This layer can itself be financial
  services firm, e.g. direct insurers. They are
  capital constrainted
• Financial intermediaries providers of informed
  capital, who possess expertise in monitoring the
  efforts of primary firms
• Outside investors providers of uninformed
  capital that could have earned market rate of
  return

5
General model

• There are a distribution of firms with asset A.
  Total capital of these firms are
• Each firm can invest in a project that demands
  for total investment of I. If IgtA, the firm needs
  external capital of I-A
• Firms affect the probability of success pH if
  they behave or pL if they shirk

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General model

• Assumptions
• Good project is socially, economically viable
• The participation of financial intermediaries can
  prevent the firm from taking B-project and move
  it to b-project. But such monitoring is costly
  with cgt0. To ensure the intermediaries to behave
  themselves, they will need to invest Km and enjoy
  the rate of return of ß

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General model

• The firms can obtain direct finance from
  uninformed investors without intermediaries. In
  this case, they invest all their own fund A and
  get I-A from outsiders
• If the project suceeds, total return is
• The necessary condition for direct finance is

8
General model

• The necessary and sufficient condition for
  outside financing is that the pledgeable expected
  income cannot be less than what they can earn
  from open market
• This condition defines a threshold level of firm
  capital below which firms cannot get external
  financing
• The next step is to work out the contribution of
  intermediary financing (move B to b)

9
General model

• The total payoff is
• The firm incentive constraint is now
• Intermediary should also have incentive
• The pledgeable expected income for investors

10
General model

• Cost of uninformed capital is lower than that of
  intermediary as to induce intermediary to
  participate
• Firms would prefer uninformed capital to
  intermediary
• So we can define the minimum level of firm
  capital that can induce the participation of
  intermediary

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• There are three types of firms in the population
  with different level of initial capital
• If , intermediary can play a role,
  requiring
• Intermediary provides a bridging loan to help
  capital constrained firms get external financing

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Implications

• This framework was proposed by Holmstrom and
  Tirole (1997) to analyse the different
  liquidity-caused recessions (1) credit crunch
  (2) collateral squeeze (3) savings squeeze
• The value of financial intermediaries is its
  ability to reduce moral hazard (or improve
  efficiency of the primary layer). Solvency ratios
  of primary firm have ignored this picture in
  prudential regulation
• Intermediaries increase the leverge of primary
  layer and improve overall efficiency. They,
  instead of firms, should be the target bodies for
  government subsidy

13
Applications

• Plantin (2006) extends this framework and propose
  a theory of the existence of specialized
  reinsurers
• The feature of the modified model is that
  intermediary firms (reinsurers) are born from
  within endogeneously arose from the primary
  layers
• Primary insurers are short of capital and they
  need reinsurers capacity to bridge and tap to
  external financing

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Reinsurance model

• Some insurers are capital constrained
• Plantin (2006) proposition 1 implies that these
  firms release their capital and become
  professional reinsurers. Let ?be the proportion
  of these firms and define aas cession rate
• Let RI and RR be the return to direct and
  reinsurers

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Reinsurance model

• RI is maximized subject to

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Reinsurance model

• If outside capital is involved,
• Substituting the constraints, one can show that
• and equilibrium cession rate (demand for
  reinsurance) is the positive root of this
  quadratic function

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Reinsurance model

• Plantin (2006) shows that the cession rate a
  increases in I, c and ? and decrease in A
• The intuitions are simple but one can image
• I the exogenous capital adequacy requirement
• c the value of monitoring or expertise per unit
  of informed capital
• ? market cost of capital
• A initial capital position of insurers
• The behaviour of cession rate is largely in line
  with real world situation

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Unresolved questions

• Plantin (2006) paper is that the value
  proposition of specialised reinsuers are their
  ability to curb direct insurers model hazard
  which is probably not what is a popular
  understanding in the market
• Another limitation is that in the real world
  specialized reinsurers are those well capitalized
  instead of residual capitalists that were left
  out from the direct market
• If the capacity of reinsurers (capital position)
  is actually larger than primary insurers, why
  dont we see they acquire all primary insurers?