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This paper analyzes the pricing of collateralized derivatives, i.e. contractswhere counterparties are not only subject to financial derivatives cash flowsbut also to collateral cash flows arising from a collateral agreement. We dothis along the lines of the brilliant approach of the first part of Moreni andPallavicini (2017): in particular we extend their framework where underlyingsare continuous processes driven by a Brownian vector, to a more general setupwhere underlyings are semimartingales (and hence jump processes). First of all,we briefly derive from scratch the theoretical foundations of the mainsubsequent achievements i.e. the extension of the classical No-Arbitrage theoryto dividend paying semimartingale assets, where by dividend we mean any cashflow earned/paid from holding the asset. In this part we merge, in the sametreatment and under the same notation, the principal known results with someoriginal ones. Then we extend the approach of Moreni and Pallavicini (2017) indifferent directions and we derive not only the pricing formulae but also thedynamics and forward prices of collateralized derivatives (extending theachievements of the first part of Gabrielli et al. (2019)). Finally, we studysome important applications (Repurchase Agreements, Securities Lending andFutures contracts) of previously established theoretical frameworks, obtainingsome results that are commonly used in practitioners literature, but often notwell understood.

No-Arbitrage Pricing, Dynamics and Forward Prices of Collateralized Derivatives