# Risk-neutral pricing the "un"guaranteed benefits of an insurance policy

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"?

Risk-neutral methods are also significantly used to calculate the Market-Consistent Enterprise Value (MCEV) of an insurer, which nowadays is one of the standard ways to measure the value of an insurance company $$-$$ see for example this Wikipedia article for a few more details on market-consistent valuation. There is also plenty of material on the internet.