Risk-neutral valuation under differential funding costs, defaults and collateralization

TL;DR

This paper presents a comprehensive valuation framework that integrates credit risk, collateralization, and funding costs, unifying different approaches to better understand derivative pricing under complex financial conditions.

Contribution

It develops a general theoretical model that unifies adjusted cash flows and replication approaches, extending previous models to broader settings including defaults and funding costs.

Findings

Unified valuation theory incorporating credit risk, collateral, and funding costs.

Clarifies the relationship between adjusted cash flows and replication approaches.

Encompasses most previous specific valuation models.

Abstract

We develop a unified valuation theory that incorporates credit risk (defaults), collateralization and funding costs, by expanding the replication approach to a generality that has not yet been studied previously and reaching valuation when replication is not assumed. This unifying theoretical framework clarifies the relationship between the two valuation approaches: the adjusted cash flows approach pioneered for example by Brigo, Pallavicini and co-authors ([12, 13, 34]) and the classic replication approach illustrated for example by Bielecki and Rutkowski and co-authors ([3, 8]). In particular, results of this work cover most previous papers where the authors studied specific replication models.