# 12

# Liquidity risk and the cost of funding in derivative contracts

## 12.1 PRICING OF DERIVATIVE CONTRACTS UNDER COLLATERAL AGREEMENTS

The liquidity risk embedded in derivative contracts requires careful analysis because of the complex nature of payoffs and of cash flow profiles. For derivative contracts too the general principle is that the value at inception should be the present value of all future (expected) cash flows, and it should be zero in order to be defined “fair”. All costs and remuneration for risks must be included in the fair value to one of the parties involved,^{1} hence funding costs and remuneration for liquidity risks have to be considered as well.

Funding costs arise from the replication (i.e., dynamic hedging) strategy of derivative contracts, and in the first part of this chapter we will study how these costs are originated: we will investigate all the components related to funding of the replication strategy and of the collateral accounts in case the contract provides for it.

Currently, most contracts dealt in interbank OTC derivatives are collateralized. A collateral agreement is characterized by the following features, amongst others:

*Initial margin* (in some contracts defined as independent amount): This is the amount of cash (or other eligible assets, possibly illiquid) that a counterparty has to post to the other in order to cover potential negative exposure of the derivative contract. It is usually related to as the VaR of the deal and theoretically should ...