Abstract
We consider a European and American put option defined on pure
endowment insurance and risk insurance contracts, respectively. These
exotic options give the holder of the option or the beneficiary of said holder
the opportunity to exercise the options and earn the difference between the
future value of the insurance benefit discounted by a fixed interest rate- the
strike price of the option, which defined in the option contract, and the
future value of the insurance benefit discounted by the real interest rates
which the option writer achieves on the investments through the exercise
date. The randomness of the interest rate is modulated by two stochastic
processes: the Ornstein-Uhlenbeck (OU) process and the Vasicek process.
In each case considered, an explicit expression of the value of the option
contract is given, as are numerical examples.
endowment insurance and risk insurance contracts, respectively. These
exotic options give the holder of the option or the beneficiary of said holder
the opportunity to exercise the options and earn the difference between the
future value of the insurance benefit discounted by a fixed interest rate- the
strike price of the option, which defined in the option contract, and the
future value of the insurance benefit discounted by the real interest rates
which the option writer achieves on the investments through the exercise
date. The randomness of the interest rate is modulated by two stochastic
processes: the Ornstein-Uhlenbeck (OU) process and the Vasicek process.
In each case considered, an explicit expression of the value of the option
contract is given, as are numerical examples.
| Original language | English |
|---|---|
| Pages (from-to) | 1-15 |
| Number of pages | 15 |
| Journal | ARCH-Actuarial Research Clearing House |
| Volume | 2 |
| State | Published - 2006 |