Funding beyond Discounting: Collateral Agreements and Derivatives Pricing

Vladimir Piterbarg

Standard derivatives pricing theory (see, for example, Hull 2006) relies on the assumption that we can borrow and lend at a unique risk-free rate. The realities of being a derivatives desk at the time of writing are, however, rather different, as historically stable relationships between bank funding rates, government rates, the London Interbank Offered Rate (Libor), etc, have broken down.

The practicalities of funding, that is, how dealers borrow and lend money, are of central importance to derivatives pricing, because replicating naturally involves borrowing and lending money and other assets. In this chapter, we establish derivatives valuation formulas in the presence of such complications starting from first principles, and study the impact of market features such as stochastic funding and collateral posting rules on values of fundamental derivatives contracts, including forwards and options.

Simplifying considerably, we can describe a derivatives desk’s activities as selling derivatives securities to clients while hedging them with other dealers. Should the desk default, a client would join the queue of the bank’s creditors. The situation is a bit different for trading