értekezés - Budapesti Corvinus Egyetem

2. függelék - Likviditáskockázat és a Korn [2003] modell
The studies by Zhou [1998], Mello and Parsons [2000], and Deep [2002] show that
liquidity risk as a result of futures with continuous marking-to-market can severely
influence optimal hedging strategies. In the context of a continuous-time equilibrium
model of futures prices, Zhou [1998] – for example – investigates the hedging decisions of
commodity producers who are faced with the constraint that their trading losses in the
futures market cannot exceed a pre-specified level, and derives the producer’s optimal
dynamic hedging strategy under the assumption of a logarithmic utility function. Mello and
Parsons [2000] develop a model of a firm with limited borrowing capacity. They analyze
how different hedging strategies with different expected liquidity needs affect firm values.
Korn [2003], on the other hand, focuses on the liquidity needs resulting from the
revaluation of forward contracts prior to maturity and the collateral calls in case of losses.
Forwards differ substantially from futures with respect to liquidity consequences. Forwards
are valued less frequently than futures over the maturity period. 162 Moreover, forwards
cause cash outflows in the case of losses due to the financing of collateral purchases, but
they do not cause cash inflows in the case of gains. Thus, in contrast to futures, forwards
can be asymmetric with respect to liquidity consequences prior to maturity. 163 Since
empirical evidence confirms that forward contracts are the predominant hedging
instruments for many non-financial firms 164 , I give a synopsis on the findings of Korn
[2003] with regards to the costs of liquidity risk below.
The crucial feature of Korn’s [2003] model is that the firm must cover accumulated losses
on its forward position with collateral. If the firm faces a positive credit spread on its
funding, but receives only the risk free rate of return on its collateral, hedging has
additional financing costs. Korn [2003] shows that firms with zero credit spreads choose to
162 In practice, firms can choose whether they want to specify a margining clause in their OTC forward
contracts that operates similarly to futures contracts with respect to marking-to-market, although with
discrete ranges of mark-to-market settlements, or firms can ask for credit lines. In latter case, the resulting
higher credit risk will be priced in the derivative, and there will be no cash call until the credit line is fully
exploited.
163 If gains have occurred on the forward position, the firm’s counterparty in the forward market might be
obliged to provide collateral, however, our firm will not receive any cash inflows associated with the
collateral.
164 See, for example, Bodnar/Hayt/Marston [1998], or Bodnar/Gebhardt [1999].
163