Funding Valuation Adjustment Research Articles

EFFICIENT WRONG-WAY RISK MODELING FOR FUNDING VALUATION ADJUSTMENTS

Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modeling. Yet, the standard assumption is independence between market risks and the counterparty defaults and funding costs. This typical industrial setting is our point of departure, where we aim to assess the impact of WWR without running a full Monte Carlo simulation with all credit and funding processes. We propose to split the exposure profile into two parts: an independent and a WWR-driven part. For the former, exposures can be re-used from the standard xVA calculation. We express the second part of the exposure profile in terms of the stochastic drivers and approximate these by a common Gaussian stochastic factor. Within the affine setting, the proposed approximation is generic, is an add-on to the existing xVA calculations and provides an efficient and robust way to include WWR in FVA modeling. Case studies for an interest rate swap and a representative multi-currency portfolio of swaps illustrate that the approximation method is applicable in a practical setting. We analyze the approximation error and use the approximation to compute WWR sensitivities, which are needed for risk management. The approach is equally applicable to other metrics such as Credit Valuation Adjustment.

Relevance of Wrong-Way Risk in Funding Valuation Adjustments

In March 2020, the world was thrown into financial distress. This manifested itself in increased uncertainty in the financial markets. Many interest rates collapsed, and funding spreads surged significantly, which increased due to the market turmoil. In light of these events, it is essential to understand and model Wrong-Way Risk (WWR) in a Funding Valuation Adjustment (FVA) context. WWR may currently be absent from FVA calculations in banks’ Valuation Adjustment (xVA) engines. However, in this letter, we demonstrate that WWR effects are non-negligible in FVA modelling from a risk-management perspective. We look at the impact of various modelling choices, such as including the default times of the relevant parties, as well as stochastic and deterministic funding spreads. A case study is presented for interest rate derivatives.

Distributionally Robust XVA via Wasserstein Distance: Wrong Way Counterparty Credit and Funding Risk

This paper investigates calculations of robust X-Value adjustment (XVA), in particular, credit valuation adjustment (CVA) and funding valuation adjustment (FVA), for over-the-counter derivatives under distributional ambiguity using Wasserstein distance as the ambiguity measure. Wrong way counterparty credit risk and funding risk can be characterized (and indeed quantified) via the robust XVA formulations. The simpler dual formulations are derived using recent Lagrangian duality results. Next, some computational experiments are conducted to measure the additional XVA charges due to distributional ambiguity under a variety of portfolio and market configurations. Finally some suggestions for further work are discussed.

Risk Managing the LIBOR Transition

By halting the LIBOR's publication, large volumes of fixed income securities, from loans to derivatives, will fall back to an alternative fixing reference. The initial proposal of a SOFR fallback eliminated any degree of subjectivity but opened up funding risk. Overlaying a credit spread over SOFR is a remedy that goes in the right direction, but neither guarantees a robust hedge for funding risk nor prevents accidental wealth transfers. To ensure robust funding risk hedges under all scenarios, we propose to complement the fallback rate by overlaying it with periodic exchanges of Funding Valuation Adjustment (FVA) reset amounts. Our proposal accomplishes the LIBOR indexing’s mandate of transferring banks’ funding risk to counterparties more accurately and robustly than the LIBOR itself while being objective and legally robust. We conclude that the LIBOR transition is an excellent stimulus and opportunity to improve funding strategies and, if implemented with foresight, can make the financial system more resilient and efficient.

An Elementary Approach to the Fundamental Theorems of Asset Pricing in Jump-Diffusion Markets with Credit Risks, Funding Risks, and Collateral

We present an elementary approach to fundamental theorems of asset and derivative pricing for a wide class of jump-diffusion markets in which there are credit risks, funding risks, and collateral. The approach yields new and intuitive proofs of both the first and second Fundamental Theorems of Asset Pricing. We give examples of how the framework incorporates the gamut of industry pricing techniques from simple Black-Scholes pricing to recent results known as Funding Valuation Adjustments (FVA). The main contribution is the insight and intuition into the nature of the fundamental theorems that is afforded by the simplicity of the setup and the consequent reliance on only the most basic results from linear algebra.

Funding Value Adjustments

ABSTRACTIn 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 adjust for FVAs. Our case studies include interest‐rate swap FVAs and violations of covered interest parity. Contrary to current valuation practice, FVAs are not themselves components of the market values of the positions being financed. Current dealer practice does, however, align incentives between trading desks and shareholders. We also establish a pecking order for preferred asset financing strategies and provide a new interpretation of the standard debit value adjustment.

The Missing Term in the FVA Calculation

In the aftermath of the Global Financial Crisis, many large banks moved to include Funding Value Adjustment (FVA) in their derivative valuations, despite controversy in the industry over its appropriateness. This paper examines the mathematical derivations of FVA-inclusive valuation formulas in an influential paper advocating FVA inclusion and identifies an implicit assumption that is unrealistic yet crucial, and hence creates problems for the derivation. We examine what happens when the assumption is abandoned and find that it can still be theoretically sound to include FVA in valuations, and to use formulas derived in the paper, subject to some modifications in either the discount rates used, or in what other valuation adjustments are included. Different types of FVA calculation are appropriate when the valuation is from a shareholder-only perspective from when it is from a whole-of-bank perspective (ie including the interests of debtholders). It is also observed that a bank that uses what are here termed 'full-FVA-inclusive valuations', may find that, in cases where the FVA is an asset, prudential supervisors require them to deduct that asset from measures of prudential capital such as CET1.

Credit contingent interest rate swap pricing

Credit value adjustment (CVA) is an adjustment to an existing trading price based on the counterparty-risk premium. Currently, CVA is computed with an implicit assumption that the replacement contract is default-free after the original counterparty defaults, with the assumption that those trades will not re-assigned. In the actual counterparty default settlement, it is the norm that trades will be re-assigned, especially on the buy side. Since the counterparty of the replacement contract could also default within the lifetime of an existing contract, ignoring the possibility of counterparty defaults of replacement contracts will either under or over estimate the cost of the risk. An important practical question is, therefore, how to estimate under/over pricing of CVA under current practice.In this paper, we considered the pricing of credit contingent interest rate swap (CCIRS) or credit contingent default swap (CCDS), which is considered the CVA hedge for interest rate swaps (IRS). We derived partial differential Eqs. (PDEs) satisfied by the approximated CVA with the assumption that the replacement contracts do not default. For comparison purposes, we also derived the PDEs for the cost of CVA by relaxing the assumption of default-free replacement contracts with a finite number of counterparty defaults. It shows that the no-default and two default cases can be derived within the same analytical solution framework, similar to the Funding Valuation Adjustment (FVA) problem where continuous funding is a reasonable assumption. The finite number of default case is non-trivial. The PDE for the two default case is derived in this paper.We calibrate our model based on market data and carry out extensive computations for the purpose of comparing these three CVAs. Our basic finding is that the values of the two CVAs are close for top rated counterparties. On the other hand, for counterparties with lower credit ratings, the difference among the two CVAs can be significant.

Derivatives and Funding Value Adjustments: A Simple Corporate Finance Approach

In the aftermath of the GFC, banks have adjusted their books of derivatives for funding costs and have made Funding Valuation Adjustments (FVA). These adjustments are surprising for two reasons. First, they are made on a voluntary basis. They are neither imposed by banking regulation nor suggested by accounting guidelines. Second, there are controversial within the academic community. The issue of whether the valuation of derivatives should account for funding costs has been highly debated in the recent years and remains unsettled. The goal of paper is to suggest a simple corporate finance approach to assess and illustrate the impact of funding costs on the valuation of derivatives and on the value of a dealer bank. In line with the conclusions of Hull and White (2012, 2014) and Andersen, Duffie and Song (2016), among others, it argues that the funding of derivative contracts leaves the bank value unaffected and that derivatives’ valuation should not be adjusted for funding costs or benefits. The paper highlights the issues of wealth transfers between the shareholders and the creditors, and raises the issues of conflicts of interests between derivatives dealers, creditors, and the bank’s shareholders.

Impact of multiple curve dynamics in credit valuation adjustments under collateralization

We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework presented in Pallavicini et al. [Funding valuation adjustment: FVA consistent with CVA, DVA, WWR, collateral, netting and re-hyphotecation, 2011], and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that spot Libor rates are to be treated as market primitives rather than being defined by no-arbitrage relationships. We formulate a consistent realistic dynamics for the different rates emerging from our analysis and compare the resulting model performances to simpler models used in the industry. We include the often neglected margin period of risk, showing how this feature may increase the impact of different rates dynamics on valuation. We point out limitations of multiple curve models with deterministic basis considering valuation of particularly sensitive products such as basis swaps. We stress that a proper wrong way risk analysis for such products requires a model with a stochastic basis and we show numerical results confirming this fact.

Internal Valuation of Assets with Liquidity Risk

FVA, funding valuation adjustment, is a new and controversial adjustment to the value of a firm’s derivatives position, joining CVA (credit valuation adjustment) and DVA (debt valuation adjustment), both of which attempt to account for the effects of counterparty credit risk on the value of a contract on a firm’s books. FVA adjusts for the fact that an investor who holds a security but finances it in the money market will have to pay a premium over the riskless rate in order to do so. This premium reduces the investment value of the position by an amount that is supposed to be captured by the FVA. The problem that Nauta raises is that this treatment does not distinguish between a security that is traded in a liquid market and can be sold for its fair value at any time, meaning overnight funding is OK, versus an illiquid security that must be financed through maturity. The article shows how this key difference translates into a liquidity-based FVA and an optimal funding horizon for less than perfectly liquid assets. <b>TOPICS:</b>Counterparty risk, quantitative methods, credit risk management

On Liquidity Risk, Funding Costs, and the Valuation of Assets

The inclusion of funding costs in the valuation of derivatives resulting in the so-called funding valuation adjustment (FVA) is a topic of intense debate, model development, and research. One issue with standard formulations of FVA is that it is the same for liquid and illiquid assets. Even if assets can be liquidated in a matter of days without discount, FVA implies that funding costs for the full term are included in the valuation. This paper studies the effect of liquidity risk on the valuation of assets through a simple model. This model assumes a Poisson process for liquidity stress events (LSEs) of random duration. In an LSE, a bank needs to liquidate an asset if the funding term is not sufficient to keep the asset funded throughout the LSE. We show that this model generates an FVA and liquidity spread. Both vanish when the asset is perfectly liquid. It is also possible to determine an optimal funding term in this model.

Uncollateralised Interest Rate Swap xVA

Derivative valuation adjustments (xVA) have been an evolving topic over the past decade, now giving us a rich theory of what was traditionally referred to as the relatively opaque "credit spread" imposed by banks. As independent risk advisors, we are regularly positioned between clients and their banks, considering the impacts of both parties' xVA when entering into and terminating positions. This paper documents our implementation of xVA modelling at the time of writing, specifically for the derivatives which our clients trade the most: uncollateralised interest rate swaps. It is also one of the first open demonstrations of an independent party modelling banks' xVA at levels actually observed by them. We focus on the most significant credit (CVA), funding (FVA) and capital (KVA) valuation adjustments. Our full modelling framework and its calibration are described and examples are given for swaps under the Standardised Approach (SA-CCR) capital framework, effective 1 January 2017.

A bond consistent derivative fair value

In this paper we present a rigorously motivated pricing equation for derivatives, including general cash collateralization schemes, which is consistent with quoted market bond prices. Traditionally, there have been differences in how instruments with similar cash flow structures have been priced if their definition falls under that of a financial derivative versus if they correspond to bonds, leading to possibilities such as funding through derivatives transactions. Furthermore, the problem has not been solved with the recent introduction of Funding Valuation Adjustments in derivatives pricing, and in some cases has even been made worse. In contrast, our proposed equation is not only consistent with fixed income assets and liabilities, but is also symmetric, implying a well-defined exit price, independent of the entity performing the valuation. Also, we provide some practical proxies, such as first-order approximations or basing calculations of CVA and DVA on bond curves, rather than Credit Default Swaps.

Unveiling FVA: Simple Cash Flows Analysis with Counterparty and Own Default for Funding Value Adjustment

In this paper, we study cash flows attached to derivative transactions including funding and collateral margin operations. Default risk of both counterparties are taken into account. We find that there is no double counting between FVA (FBA) and DVA. We give an algorithm to calculate FVA in the Least Squares Monte Carlo framework.

FVA and CVA for Collateralized Trades with Re-hypothecation

Through this article we join the ongoing “FVA debate” with a strategy of bilateral replication, which enables us to price derivatives trades and identify XVAs, including the FVA. We let the issuer and buyer replicate the derivative's payoffs and the loss given the issuer's default, respectively, while taking into account the costs of funding for replication and collateral posting in the replicating portfolios. The strategy leads to a PDE for the economic value of the derivative, and the PDE also implies the unique risk-neutral pricing measure. A proper solution of the PDE gives rise to a decomposition of the derivatives economic value into the risk-free value of the derivative, the credit valuation adjustment, and the funding valuation adjustment. We show that in general the economic values to the two trading parties are different, due to the different funding needs and funding costs, and both parties may have to bear some funding costs in order to strike a deal. When the premium for buying a derivatives asset is also funded, then to the buyer the trade actually consists of two transactions: borrowing and purchasing, and the FVA for the trade can be obtained by separately evaluating the FVAs of the two transactions.

Multi-Curve Discounting

We introduce the multi-curve discounting (MCD) method, where the discount curve depends on the liquidity horizon of the asset. The difference between the value of an asset using OIS discounting and a discount curve referencing the liquidity horizon can be interpreted as a Funding Valuation Adjustment (FVA). We show that a simple model for liquidity risk implies MCD. The liquidity risk model formulation clarifies how a non-zero FVA occurs without violating the Modigliani-Miller theorem.

Funding Value Adjustments

We demonstrate that large funding value adjustments (FVAs) being made by derivatives dealers to the disclosed valuations of their swap books are not consistent with any coherent notion of fair market value. Essentially the same funding cost adjustment is a reduction in the dealer's equity value. This reduction in equity value is exactly offset by the sum of an upward adjustment to a dealer's debt valuation (as a wealth transfer from shareholders) and a change in the present value of the dealer's financial distress costs. While others have already suggested that FVA accounting suffers from coherence problems, this paper is the first to identify and characterize these problems in the context of a full structural model of a dealer's balance sheet. In addition to giving an appropriate theoretical foundation for funding value adjustments, our model shows how dealers' bid and ask quotes should be adjusted so as to compensate shareholders for the impact of both funding costs and the dealer's own default risk. We also establish a pecking order for preferred swap financing strategies, characterize the valuation effects of initial margin financing (known as MVA), and provide a new interpretation of the standard debit value adjustment (DVA).

Collateral and PDE

After Lehman default (credit crisis 2007), practitioners considered the default risk as a major risk. The regulators pushed the industry to use collateral in order to reduce the risk. In this new world, we want to see how this new considerations affect the theory related to the Partial Differential Equation (PDE) pricing methodology. First, we consider a theoretical framework introduced by Piterbarg, then we relax the perfect collateralisation assumption and establish the correct derivation of the hedgingportfolio.We do not intent to offense anyone and recognise fully the work done in the building of the Post Lehman Theory.We establish different PDE forms dependent of the treasury management strategy and also retrieve Kamtchueng results for the Funding Valuation Adjustment. Indeed there are differences between Funding charge coming from the cash flows due and the funding cost strategy resulting of cash and trading desks.

Capital Valuation Adjustment and Funding Valuation Adjustment

Capital Valuation Adjustment and Funding Valuation Adjustment