A commenter comments.
If your theories are correct, it is Eumaeus who should be
able to make unlimited arbitrage profits if the matching adjustment is mis-pricing. Why have you not done this? The answer is that outside the university classroom, arbitrage is not possible for illiquid assets / liabilities.
Eumaeus replies
On the contrary, arbitrage is easy. (1) Borrow from pensioners at close to risk free through the buyout market, receive payment in safe assets (2) replace safe assets with higher yielding ones (3) persuade PRA that some or all of the spread on higher yielding assets is risk free (4) discount liabilities at the higher rate and create capital (5) when you have created enough capital, distribute some of it to owners.
I.e. Matching Adjustment is an effective a way of shorting the illiquid asset. You have bought the illiquid at market price, including the ‘illiquidity premium’, although it is difficult to prize away the illiquidity element from the market risky element. Then, by discounting your illiquid riskless pension liability at higher than risk free, you have beautifully captured that illiquidity spread. Arbitrage courtesy of PRA, thank you regulators!