| dc.description.abstract | Many insurance companies sell products that involve embedded options. The value of such an option
represents the expected future liability and therefore it is important that insurers can value the options
they sold. Since most of these options are very complex, they are valued using Monte Carlo simulations.
This requires considerable computation resources and therefore methods have been developed to approx-
imate the option values analytically. In this thesis we study two of these options and give analytical
approximations for their values. The first option is a guarantee in unit-linked insurance for which upper
and lower bounds are derived using the concept of comonotonicity as developed by Dhaene, Denuit,
Goovaerts, Kaas and Vyncke (2002a, 2002b). This is done in the Black-Scholes model as well as in the
Hull-White-Black-Scholes model, where the latter has the additional feature of stochastic interest rates.
The lower bound is the same as derived in Schrager and Pelsser (2004), but the derivation by explicitly
applying the concept of comonotonicity was not given before. The second option is a call option on an
average of swap rates as used in profit sharing. The value is approximated by using approximate swap
rate dynamics as developed by Schrager and Pelsser (2006). Finally, the quality of the approximations
is determined by comparing them to Monte Carlo simulations. It turns out that the lower bound for the
guarantee in unit-linked insurance is a very accurate approximation. | |
