Craig Turnbull’s article on Matching Adjustment repays close attention
Two fairly deep questions, namely (1) why insurance firms often have a non-zero risk appetite for the assets held to back insurance liabilities, and (2) what is the purpose of solvency regulation.
I am not sure whether Craig satisfactorily answers those questions, however he makes some interesting points along the way. For example,
… no model in use by actuaries or other financial risk managers in 2000 would have attached any probability to the interest rate environment in 2019 looking like the one we have today in many countries in the developed world; and why, to take a different example, UK actuaries’ 1990 estimate of the mortality of a 70 year-old male annuitant in 2020 is likely to be wrong by a factor of 2.
Quite.
Then he argues (section 3) that there is an alternative to defining capital requirements that does not use probability estimates for the projected future values of asset prices or cashflows, but instead defines solvency capital as “the amount of capital required such that the value of the shareholder’s default put option is limited to some specified maximum level”.
That idea ties in with some work Eumaeus has been doing on option pricing for assets with non-standard or irregular price distributions (see chart above), on which more later.