To Share or Not to Share? Uncovered Losses in a Derivatives Clearinghouse

If the payor receives the good endowment y, which occurs with probability π close to 1, the contract is honored and the payor has to transfer to the payee the contracted amount θ (θ ≤ y) using the CCP. [...] Since the contracted amount is θ, and the probability of default on the contract is 1− π, the expected uncovered loss is L = (1 − π)(1 − Φ)θ, where (1 − Φ) is the uncollateralized fraction of the position θ. I will refer to the expression κ ≡ (1− π)(1− Φ) as the uncovered default risk from the trade. [...] For the CCP to break even, the losses allocated to members must equal the aggregate expected loss from default minus any loss absorbed by the CCP’s skin in the game, s. Let p denote the probability that a survivor bank is allocated a loss of T. Then the break-even condition requires that E[Loss allocated to members] = E [Uncovered default loss] − [Skin in the game], or pT = κθ − s. (2) Since the b [...] This happens because risk-based skin in the game changes the terms of the tradeoff between the loss size and loss probability, and hence, alters the optimum trading position size. [...] Now suppose u′(x+ θ − T ) is balanced against the utility costs of trading, given by the remaining terms in equation (5) (the costs of having to pay plus the costs of collateral γΦ) and consider an exogenous increase in skin in the game s. Skin in the game reduces the loss T , thereby increasing wealth and lowering the marginal utility.