Funding beyond discounting: collateral agreements and derivatives pricing

Standard theory assumes traders can lend and borrow at a risk-free rate, ignoring the intricacies of the repo and collateralisation markets. Here, Vladimir Piterbarg shows that these force adjustments to discounting, forward prices and implied volatilities, depending on the particulars of collateral posting

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

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Funding beyond discounting: collateral agreements and derivatives pricing