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Insurance contracts, especially from business lines life and health, are of economic nature, obviously by their usual term and real hedging claim. It is impossible to replicate the complete claim at capital markets ex-ante. In contrast to pure wealth management products, customers purchase and claim a dedicated economic benefit, they at least redeem when the insured event occurs.
This essay is primarily devoted to the formulation of an option-price for economic re-investment risk, which is undertaken in the economic horizon behind the so-called last liquid point (llp). Under, for financial mathematic models, common assumptions, risk can be measured by the formula
Where c stands for aggregate contractual cash-flow, p for stochastic or expected price of the risk-free economy yield-curve, with term exceeding the llp, and Ω for the state-space.
The claim and yield-curve replicating portfolio hedges economic welfare, its inflation and real growth rate. In the qualitative component it preserves and improves customers’ level of sectorial economic welfare through risk-adjusted investment. In the quantitative component it collects the aggregate cost of capital margin for related economic welfare in prices consumers pay.
Secondarily the article wants to find answers for arising questions: What does financially rational surplus participation under the regime of the option price formula for re-investment risk look like? What is the formula’s advantage over entity simulations common under Solvency II? Is steering re-investment risk part of enterprise risk management or product component in form of a margin? How to deal with discretionary participation, as considered under IFRS 17, regarding the formula? What is the best choice for the interest rate model generating stochastic prices? Finally, again: What is the correct yield curve?
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