xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT

2020 ◽  
Vol 23 (01) ◽  
pp. 2050006
Author(s):  
LIXIN WU ◽  
DAWEI ZHANG
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Liquidity Risk ◽  
Credit Default Swaps ◽  
Interest Rate Swap ◽  
Funding Liquidity ◽  
Credit Default ◽  
Risk Neutral ◽  
Default Risks ◽  
Rate Swap

xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

scholarly journals CVA AND FVA TO DERIVATIVES TRADES COLLATERALIZED BY CASH

2015 ◽  
Vol 18 (05) ◽  
pp. 1550035 ◽  
Author(s):  
LIXIN WU
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rate ◽  
Credit Default Swaps ◽  
Call Option ◽  
Interest Rate Swap ◽  
Pricing Process ◽  
Credit Default ◽  
Credit Valuation Adjustment ◽  
Rate Swap

In this paper, we consider replication pricing of derivatives that are partially collateralized by cash. We let issuer replicate the derivatives payout using shares and cash, and let buyer replicate the loss given the counterparty default using credit default swaps. The costs of funding for replication and collateral posting are taken into account in the pricing process. A partial differential equation (PDE) for the derivatives price is established, and its solution is provided in a Feynman–Kac formula, which decomposes the derivatives value into the risk-free value of the derivative plus credit valuation adjustment (CVA) and funding valuation adjustment (FVA). For most derivatives, we show that CVAs can be evaluated analytically or semi-analytically, while FVAs as well as the derivatives values can be solved recursively through numerical procedures due to their interdependence. In numerical demonstrations, continuous and discrete margin revisions are considered, respectively, for an equity call option and a vanilla interest-rate swap.

scholarly journals Interest Rate Swap Market Complexity and Its Risk Management Implications

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-20
Author(s):  
Steve Y. Yang ◽  
Esen Onur
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Network Structure ◽  
Risk Sharing ◽  
Interest Rate Swap ◽  
Market Participants ◽  
Interest Rate Futures ◽  
The Interest Rate ◽  
Management Behaviors ◽  
Rate Swap

The primary objective of this paper is to study the post Dodd-Frank network structure of the interest rate swap market and propose a set of effective complexity measures to understand how the swap users respond to market risks. We use a unique swap dataset extracted from the swap data repositories (SDRs) to examine the network structure properties and market participants’ risk management behaviors. We find (a) the interest rate swap market follows a scale-free network where the power-law exponent is less than 2, which indicates that few of its important entities have a significant number of contracts within their subsidiaries (a.k.a. interaffiliated swap contracts); (b) swap rate volatility Granger-causes swap users to increase their risk sharing intensity at entity level, but market participants do not change their risk management strategies in general; (c) there is a significant contemporaneous correlation between the swap rate volatility and the underlying interest rate futures volatility. However, interest rate swap volatility does not cause the underlying interest rate futures volatility and vice versa. These findings provide the market regulators and swap users a better understanding of interest rate swap market participants’ risk management behaviors, and it also provides a method to monitor the swap market risk sharing dynamics.

scholarly journals Cross-Currency Interest Rate Swap Application in the Long-Term Currency Risk Management

2020 ◽  
Vol 54 (2) ◽  
pp. 113
Author(s):  
Piotr Wybieralski
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Risk Estimation ◽  
Cash Flows ◽  
Currency Risk ◽  
Money Markets ◽  
Interest Rate Swap ◽  
Risk Hedging ◽  
Rate Swap

<p>Effective currency risk management using various derivatives is particularly important under increased market volatility. The risk is relatively higher for longer than shorter time frames. This study highlights the implementation of selected instruments for long-term hedging. It presents the application of cross-currency interest rate swap as a currency risk hedging tool used by Polish exporters, mainly manufacturers generating their revenues mostly abroad (in euro area), exposed to negative exchange rate fluctuations. The paper covers issues related to the pricing, market risk estimation and collateral required in the OTC market, as well as undertakes a sensitivity analysis in search for exchange rates at which margin call occurs. There is a comparative analysis and back test simulation conducted using market data from exchange and money markets. The study emphasized that the analyzed instrument meets the expectations in terms of hedging the company cash flows, as well as may generate additional benefits due to the still existing interest rate differential.</p>

PRICING COUNTERPARTY RISK INCLUDING COLLATERALIZATION, NETTING RULES, RE-HYPOTHECATION AND WRONG-WAY RISK

2013 ◽  
Vol 16 (02) ◽  
pp. 1350007 ◽  
Author(s):  
DAMIANO BRIGO ◽  
AGOSTINO CAPPONI ◽  
ANDREA PALLAVICINI ◽  
VASILEIOS PAPATHEODOROU
Keyword(s):  
Interest Rate ◽  
Credit Derivatives ◽  
Credit Default Swaps ◽  
Credit Spread ◽  
Counterparty Risk ◽  
Default Correlation ◽  
Dynamical Models ◽  
Credit Default ◽  
The Impact

This article is concerned with the arbitrage-free valuation of bilateral counterparty risk through stochastic dynamical models when collateral is included, with possible rehypothecation. The payout of claims is modified to account for collateral margining in agreement with International Swap and Derivatives Association (ISDA) documentation. The analysis is specialized to interest-rate and credit derivatives. In particular, credit default swaps are considered to show that a perfect collateralization cannot be achieved under default correlation. Interest rate and credit spread volatilities are fully accounted for, as is the impact of re-hypothecation, collateral margining frequency, and dependencies.

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