# A unified approach to xVA with CSA discounting and initial margin

@article{Biagini2019AUA, title={A unified approach to xVA with CSA discounting and initial margin}, author={Francesca Biagini and Alessandro Gnoatto and Immacolata Oliva}, journal={Risk Management \& Analysis in Financial Institutions eJournal}, year={2019} }

In this paper we extend the existing literature on xVA along three directions. First, we enhance current BSDE-based xVA frameworks to include initial margin in presence of defaults. Next, we solve ...

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## References

SHOWING 1-10 OF 51 REFERENCES

### XVA analysis from the balance sheet

- Economics
- 2020

A cost-of-capital XVA strategy isRooted in a balance sheet perspective which is key to identifying the economic meaning of the XVA terms and can be solved efficiently using GPU computing combined with deep learning regression methods in a whole bank balance sheet context.

### Robust XVA

- EconomicsMathematical Finance
- 2020

We introduce an arbitrage‐free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in…

### Arbitrage‐free XVA

- Economics
- 2016

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…

### A Note on Construction of Multiple Swap Curves with and without Collateral

- Economics
- 2010

There are now available wide variety of swap products which exchange Libors with different currencies and tenors. Furthermore, the collateralization is becoming more and more popular due to the…

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

- Economics
- 2018

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…

### Funding Valuation Adjustment: A Consistent Framework Including CVA, DVA, Collateral, Netting Rules and Re-Hypothecation

- Economics
- 2011

In this paper we describe how to include funding and margining costs into a risk-neutral pricing framework for counterparty credit risk. We consider realistic settings and we include in our models…

### Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks

- Economics
- 2014

The introduction of Central Clearing Counterparties (CCPs) in most derivative transactions will dramatically change the landscape of derivatives pricing, hedging and risk management, and, according…

### Funding Value Adjustments

- EconomicsThe Journal of Finance
- 2018

In this paper, we demonstrate that the funding value adjustments (FVAs) of major dealers are debt overhang costs to their shareholders. To maximize shareholder value, dealer quotations therefore…

### Estimation of Future Initial Margins in a Multi-Curve Interest Rate Framework

- Economics
- 2016

We propose an approach for the dynamical estimation of initial margins. We determine initial margins at future points in time by computing a risk measure of the modelled price increment over a margin…

### Integrated Structural Approach to Credit Value Adjustment

- EconomicsEur. J. Oper. Res.
- 2019

An integrated pricing framework for Credit Value Adjustment of equity and commodity products that allows for calibration and pricing to be based on the same numerical schemes, and also allows the inclusion of risk mitigation clauses such as netting, collateral and initial margin provisions.