I'd love to know if the model of Black-Scholes-Merton could be used to anything that replicates the payoff of a call or option, for example:
An insurance contract with participation ( meaning that you can have a right to discretionary benefits, an extra something you can earn provided some conditions).
Imagine an insurance contract in which the policyholder invests 100\$ cash to receive one year later 102\$ cash. However, in a good economic scenario he can get an extra %-gain if the investments outperform the liabilities, i.e if the growth of the invested capital is higher than the growth of the liability.
If I define $S_t-K$ as the payoff of the discretionary benefits to the policy holder ( $S_t$ being the asset growth and $K$ the liability growth say some assumed fixed %) would I be able to use Black-Scholes-Merton formula for a call to get the "expected discretionary benefit"?