Fair bilateral pricing under funding costs and exogenous collateralization

Nie, Tianyang; Rutkowski, Marek

doi:10.1111/mafi.12145

Cited by 23 publications

(81 citation statements)

References 24 publications

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“…We remark that in a market model without defaultable securities, similar inequalities between borrowing and lending rates have been derived by Bielecki and Rutkowski (, proposition 3.3), and by Nie and Rutkowski (, proposition 3.4). We impose additional relations between lending rates and return rates of the risky bonds given that our model also allows for counterparty risk.…”

Section: Arbitrage‐free Valuation and Xvasupporting

confidence: 80%

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Arbitrage‐free XVA

Bichuch

Capponi

Sturm

2017

Mathematical Finance

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We develop a framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no‐arbitrage arguments, we derive backward stochastic differential equations associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buyer's and seller's XVA, which in turn identify a no‐arbitrage interval. In the case that borrowing and lending rates coincide, we provide a fully explicit expression for the unique XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. In the general case of asymmetric funding, repo, and collateral rates, we study the semilinear partial differential equations characterizing buyer's and seller's XVA and show the existence of a unique classical solution to it. To illustrate our results, we conduct a numerical study demonstrating how funding costs, repo rates, and counterparty risk contribute to determine the total valuation adjustment.

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Section: Arbitrage‐free Valuation and Xvasupporting

confidence: 80%

“…As in Piterbarg (2010), they do not take counterparty credit risk into account. Nie and Rutkowski (2018) study the existence of fair bilateral prices. A good overview of the current literature is given in Crépey, Bielecki, and Brigo (2014).…”

Section: Introductionmentioning

confidence: 99%

Arbitrage‐free XVA

Bichuch

Capponi

Sturm

2017

Mathematical Finance

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“…Given any specific semimartingale model for risky assets, it is usually possible to show that the pricing BSDE has a unique solution in a suitable space of stochastic processes. For instance, Nie and Rutkowski [30,31,32] examine the valuation and hedging of a contract (A, C) (so defaults are not considered) with both an exogenous and an endogenous collateralization.…”

Section: Conventional Valuation Adjustmentsmentioning

confidence: 99%

“…Several kinds of valuation adjustments are also discussed in [24]. As mentioned above, the rigorous theory of valuation in the presence of all such effects can be quite challenging; in general, it does not lead to an additive split in the above adjustments, but rather to nonlinear valuation paradigms that are based on advanced mathematical tools, such as semi-linear PDEs or BSDEs (see, e.g., [30,31,32]). A significant leap was achieved by the "adjusted cash flows" approach whose practical applicability led to its implementation in the industry.…”

Section: Introductionmentioning

confidence: 99%

Risk-Neutral Valuation Under Differential Funding Costs, Defaults and Collateralization

et al. 2018

Self Cite

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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 8]). In particular, results of this work cover most previous papers where the authors studied specific replication models.

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“…Bielecki and Rutkowski (2014) consider the viewpoint of the hedger, but do not derive arbitrage bounds for unilateral prices. These are instead analyzed in Nie and Rutkowski (2013), who also examine the existence of fair bilateral prices. A good overview of the current literature is given in Crépey et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Arbitrage-Free Pricing of XVA -- Part I: Framework and Explicit Examples

2015

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We develop a framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on noarbitrage arguments, we derive nonlinear backward stochastic differential equations (BSDEs) associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buyer's and seller's XVA, which in turn identify a no-arbitrage interval. In the case that borrowing and lending rates coincide, we provide a fully explicit expression for the uniquely determined XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. This extends the result of Piterbarg (2010) by incorporating the effect of premature contract termination due to default risk of the trader and of his counterparty.

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Fair bilateral pricing under funding costs and exogenous collateralization

Cited by 23 publications

References 24 publications

Arbitrage‐free XVA

Arbitrage‐free XVA

Risk-Neutral Valuation Under Differential Funding Costs, Defaults and Collateralization

Arbitrage-Free Pricing of XVA -- Part I: Framework and Explicit Examples

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