Dear friends,
Recently, I have started to study and to understand different aspects
embedded in managing portfolios of an insurance company. It turns out to be
a quite fertile field for applied mathematics and physical methods.
Indeed insurance contracts are based on a guaranteed yield over a very long
time period (5/10/20 years).
The policy holder is actually long on a percentage of the portfolio yield,
and he holds as well the equivalent of a put option which gives him the
guarantee of a minimum yield at maturity. Those options can generally be of
two kinds: European, or Cliquet. Their underlying being the portfolio's
yield itself ("Hic sunt leones"). Actually the payoff is very similar to
what is reported in the figure in attachment.
This payoff applies only at maturity in the european case and every year in
the consolidated one(or cliquet style contracts).
The scope is now to correctly price these options, to immunize the company
from the negative part of the put payoff, and to define/staisfy a given
benchmark for the equity side (benefits of the company). For this the only
parameter which can be tuned is the portfolio. A naive idea could be a
dynamic delta hedging, but
since the portfolio performance is modified by any intervention, so do all
the properties of the options. Moreover the portfolio is not some traded
quantity that you can easyly buy/sell on the market place. It seems to me
that the effects of this feedback loop are quite impredictable and the naive
approach could turn out to be useless or even dangerous.
Probably only some stochastic optimal control procedures could give
realistic results for the asset allocation. The important issue is, as
mentionned in the Prof I. Kondor in his talk in Doublin, whether to price
portfolio insurance as a combination of options or on the basis of some
passive strategy.
Does someone of you have any advice about this problem? Any good references
abut it.
I would be really very pleased if you will agree to discuss further about
this theme.
Regards,
Gabriele
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