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principles. In following paragraphs only surrender option where the
amount paid on surrender is guaranted is considered.
3.171 The surrender option is very important element for undertakings and
should be taken into account when valuing the technical provisions. It
could have significant financial effect for instance on uncharged
expenses and uncharged costs for options and guarantees.
3.172 Literature usually distinguishes two broad approaches for modelling the
surrender options that are usually assessed from an undertaking
perspective on homogeneous groups rather than from a single
policyholder’s perspective. The first approach tries to encompass in the
modelling rational behaviour of policyholders whereas the second one
tries to encompass more irrational behaviour of the policyholders.
3.173 The problem of determining the price of the surrender option in the case
of rational behaviour of policyholders could be described as an optimal
stopping time with respect to the filtration generated by the prices of the
financial assets. The price of surrender option is theoretically modelled
using the theory of stochastic processes and their optimal stopping time.
Thus it is optimal for the policyholder to surrender when realistic value of
the contract is less than or equal to the amount received by immediately
surrendering the contract. In practice the surrender option are
commonly priced recursively using numerical methods such as binomial
trees.
3.174 The argument in favour for irrational behaviour of policyholders is that
approach based on rational behaviour of policyholders in most
circumstances does not realistically model a policyholder’s surrender
behaviour and that the policyholder’s information is asymmetric. It is
rather common practice that the information about realistic value of
insurance contract that needs to be compared with surrender value is
not made in public and kept as internal information by the undertaking.
The value of surrender option from the policyholder’s perspective
depends on own information and on own risk aversion and therefore is a
subjective value different from policyholder to policyholder and is mostly
unknown for the undertaking. The problem of determining the price of
the surrender option is not defined as stopping time model and thus
more suitable for modelling realistic surrender behaviour. Thus
assumptions made on random time of surrender are rather general and
allows many ways to construct it in practice. The approaches could
consist of multifactor functions that vary with realistic value, surrender
value, age, policy duration, time to maturity, interest rate, market
volatilities, and other economic factors of importance. The dependence
on the financial market would however result in rather comprehensive
modelling more suitable for a stochastic simulation approach rather than
a simple closed-form solution.
3.175 Besides the rational or irrational behaviour of policyholders discussed in
previous paragraphs, the experience of surrenders tend to suggests that
rational reasons for movements in surrender rates are:
• quality of sales advice and whether any misselling may occur leading
to earlier surrenders in excess of later surrenders;
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