arXiv subjects

Chris Kenyon

Publications and source records attributed to Chris Kenyon.

At least 19 recordsLinked to original sources

arXiv2022

Transparency principle for carbon emissions drives sustainable finance

Alignment of financial market incentives and carbon emissions disincentives is key to limiting global warming. Regulators and standards bodies have made a start by requiring some carbon-related disclosures and proposing others. Here we go further and propose a Carbon Equivalence Principle: all financial products shall contain a description of the equivalent carbon flows from greenhouse gases that the products enable, as well as their existing description in terms of cash flows. This description of the carbon flows enabled by the project shall be compatible with existing bank systems that track cashflows so that carbon flows have equal standing to cash flows. We demonstrate that this transparency alone can align incentives by applying it to project finance examples for power generation and by following through the financial analysis. The financial requirements to offset costs of carbon flows enabled in the future radically change project costs, and risk that assets become stranded, thus further increasing costs. This observation holds whichever partner in the project bears the enabled-carbon costs. Mitigating these risks requires project re-structuring to include negative emissions technologies. We also consider that sequestered carbon needs to remain sequestered permanently, e.g., for at least one hundred years. We introduce mixed financial-physical solutions to minimise this permanence cost, and price to them. This complements previous insurance-based proposals with lesser scope. For financial viability we introduce project designs that are financially net-zero, and as a consequence are carbon negative. Thus we see that adoption of the Carbon Equivalence Principle for financial products aligns incentives, requires product redesign, and is simply good financial management driving sustainability.

q-fin.RM↗

arXiv2021

Sustainability Manifesto for Financial Products: Carbon Equivalence Principle

Sustainability is a key point for financial markets and the label "Green" is an attempt to address this. Acquisition of the label "Green" for financial products carries potential benefits, hence the controversy and attractiveness of the label. However, such a binary label inadequately represents the carbon impact - we use carbon as a useful simplification of sustainability. Carbon impact has a range either size of zero. Both carbon emissions, and sequestration of carbon, are possible results of financial products. A binary label does not allow differentiation between a carbon neutral investment and a coal power plant. Carbon impact has timing and duration, a planted forest takes time to grow, a coal power plant takes time to emit. Hence we propose the Carbon Equivalence Principle (CEP) for financial products: that the carbon effect of a financial product shall be included as a linked term sheet compatible with existing bank systems. This can either be a single flow, i.e., a summary carbon flow, or a linked termsheet describing the carbon impacts in volume and time. The CEP means that the carbon impact of investment follows the money. Making carbon impacts consistent with existing bank systems enables direct alignment of financial product use and sustainability, improving on non-compatible disclosure proposals.

q-fin.GN↗

arXiv2021

Climate Change Valuation Adjustment (CCVA) using parameterized climate change impacts

We introduce Climate Change Valuation Adjustment (CCVA) to capture climate change impacts on CVA+FVA that are currently invisible assuming typical market practice. To discuss such impacts on CVA+FVA from changes to instantaneous hazard rates we introduce a flexible and expressive parameterization to capture the path of this impact to climate change endpoints, and transient transition effects. Finally we provide quantification of examples of typical interest where there is risk of economic stress from sea level change up to 2101, and from transformations of business models. We find that even with the slowest possible uniform approach to a climate change impact in 2101 there can still be significant CVA+FVA impacts on interest rate swaps of 20 years or more maturity. Transformation effects on CVA+FVA are strongly dependent on timing and duration of business model transformation. Using a parameterized approach enables discussion with stakeholders of economic impacts on CVA+FVA, whatever the details behind the climate impact.

q-fin.PR↗

arXiv2020

Client engineering of XVA in crisis and normality: Restructuring, Mandatory Breaks and Resets

Crises challenge client XVA management when continuous collateralization is not possible because a derivative locks in the client credit level and the provider's funding level, on the trade date, for the life of the trade. We price XVA reduction strategies from the client point of view comparing multiple trade strategies using Mandatory Breaks or Restructuring, to modifications of a single trade using a Reset. We analyse previous crises and recovery of CDS to inform our numerical examples. In our numerical examples Resets can be twice as effective as Mandatory Break/Restructuring if there is no credit recovery. When recovery is at least 1/3 of the credit shock then Mandatory Break/Restructuring can be more effective.

q-fin.PR↗

arXiv2020

Model independent WWR for regulatory CVA and for accounting CVA and FVA

General wrong way risk (WWR) estimation is necessary for regulatory CVA capital and useful for pricing CVA and FVA. We introduce a model independent method for calculating WWR and update the definition of WWR to deal with the lack of replication instruments (calibration data) transparently. This model independent approach is extremely simple: we just re-write the CVA and FVA integral expressions in terms of their components and then calibrate these components. This provides transparency between component calibration and CVA/FVA effect because there is no model interpretation in between. Including funding in WWR means that there are now two WWR terms rather than the usual one. Using a regulatory inspired calibration from MAR50 we investigate WWR effects for vanilla interest rate swaps and show that the WWR effects for FVA are significantly more material than for CVA. This model independent approach can also be used to compare any WWR model by simply calibrating to it for a portfolio and counterparty, to demonstrate the effects of the model under investigation in terms of components of CVA/FVA calculations.

q-fin.PR↗

arXiv2019

Revising SA-CCR

From SA-CCR to RSA-CCR: making SA-CCR self-consistent and appropriately risk-sensitive by cashflow decomposition in a 3-Factor Gaussian Market Model

q-fin.RM↗

arXiv2018

Counterparty Trading Limits Revisited:CSAs, IM, SwapAgent(r), from PFE to PFL

The utility of Potential Future Exposure (PFE) for counterparty trading limits is being challenged by new market developments, notably widespread regulatory Initial Margin (using 99% 10-day exposure), and netting of trade and collateral flows. However PFE has pre-existing challenges w.r.t. portfolios/distributions, collateralization, netting set seniority, and overlaps with CVA. We introduce Potential Future Loss (PFL) which combines expected shortfall (ES) and loss given default (LGD) as a replacement for PFE. With two additional variants Adjusted PFL (aPFL) and Protected Adjusted PFL (paPFL) these deal with both new and pre-existing challenges. We provide a theoretical background and numerical examples.

q-fin.RM↗

arXiv2018

Behavioural effects on XVA

Bank behaviour is important for pricing XVA because it links different counterparties and thus breaks the usual XVA pricing assumption of counterparty independence. Consider a typical case of a bank hedging a client trade via a CCP. On client default the hedge (effects) will be removed (rebalanced). On the other hand, if the hedge counterparty defaults the hedge will be replaced. Thus if the hedge required initial margin then the default probability driving MVA is from the client not from the hedge counterparty. This is the opposite of usual assumptions where counterparty XVAs are computed independent of each other. Replacement of the hedge counterparty means multiple CVA costs on the hedge side need inclusion. Since hedge trades are generally at riskless mid (or worse) these costs are paid on the client side, and must be calculated before the replacement hedge counterparties are known. We call these counterparties anonymous counterparties. The effects on CVA and MVA will generally be exclusive because MVA largely removes CVA, and CVA is hardly relevant for CCPs. Effects on KVA and FVA will resemble those on MVA. We provide a theoretical framework, including anonymous counterparties, and numerical examples. Pricing XVA by considering counterparties in isolation is inadequate and behaviour must be taken into account.

q-fin.PR↗

arXiv2016

XVA at the Exercise Boundary

XVA is a material component of a trade valuation and hence it must impact the decision to exercise options within a given netting set. This is true for both unsecured trades and secured / cleared trades where KVA and MVA play a material role even if CVA and FVA do not. However, this effect has frequently been ignored in XVA models and indeed in exercise decisions made by option owners. This paper describes how XVA impacts the exercise decision and how this can be readily evaluated using regression techniques (Longstaff and Schwartz 2001). The paper then assesses the materiality of the impact of XVA at the exercise boundary on swaption examples.

q-fin.PR↗

arXiv2016

Option-Based Pricing of Wrong Way Risk for CVA

The two main issues for managing wrong way risk (WWR) for the credit valuation adjustment (CVA, i.e. WW-CVA) are calibration and hedging. Hence we start from a novel model-free worst-case approach based on static hedging of counterparty exposure with liquid options. We say "start from" because we demonstrate that a naive worst-case approach contains hidden unrealistic assumptions on the variance of the hazard rate (i.e. that it is infinite). We correct this by making it an explicit (finite) parameter and present an efficient method for solving the parametrized model optimizing the hedges. We also prove that WW-CVA is theoretically, but not practically, unbounded. The option-based hedges serve to significantly reduce (typically halve) practical WW-CVA. Thus we propose a realistic and practical option-based worst case CVA.

q-fin.PR↗

arXiv2015

Which measure for PFE? The Risk Appetite Measure, A

Potential Future Exposure (PFE) is a standard risk metric for managing business unit counterparty credit risk but there is debate on how it should be calculated. The debate has been whether to use one of many historical ("physical") measures (one per calibration setup), or one of many risk-neutral measures (one per numeraire). However, we argue that limits should be based on the bank's own risk appetite provided that this is consistent with regulatory backtesting and that whichever measure is used it should behave (in a sense made precise) like a historical measure. Backtesting is only required by regulators for banks with IMM approval but we expect that similar methods are part of limit maintenance generally. We provide three methods for computing the bank price of risk from readily available business unit data, i.e. business unit budgets (rate of return) and limits (e.g. exposure percentiles). Hence we define and propose a Risk Appetite Measure, A, for PFE and suggest that this is uniquely consistent with the bank's Risk Appetite Framework as required by sound governance.

q-fin.RM↗

arXiv2015

Dirac Processes and Default Risk

We introduce Dirac processes, using Dirac delta functions, for short-rate-type pricing of financial derivatives. Dirac processes add spikes to the existing building blocks of diffusions and jumps. Dirac processes are Generalized Processes, which have not been used directly before because the dollar value of non-Real numbers is meaningless. However, short-rate pricing is based on integrals so Dirac processes are natural. This integration directly implies that jumps are redundant whilst Dirac processes expand expressivity of short-rate approaches. Practically, we demonstrate that Dirac processes enable high implied volatility for CDS swaptions that has been otherwise problematic in hazard rate setups.

q-fin.PR↗

arXiv2015

MVA: Initial Margin Valuation Adjustment by Replication and Regression

Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg 2010, Piterbarg2012), under counterparty risk with unsecured funding costs (FVA) (Burgard2011, Burgard2011, Burgard2013) and in the presence of regulatory capital (KVA) (Green2014) are established through valuation adjustments, hitherto initial margin has not been considered. This paper further extends the semi-replication framework of (Burgard2013a), itself later extended by (Green2014), to cover the cost of initial margin, leading to Margin Valuation Adjustment (MVA). Initial margin requirements are typically generated through the use of VAR or CVAR models. Given the form of MVA as an integral over the expected initial margin profile this would lead to excessive computational costs if a brute force calculation were to be used. Hence we also propose a computationally efficient approach to the calculation of MVA through the use of regression techniques, Longstaff-Schwartz Augmented Compression (LSAC).

q-fin.PR↗

arXiv2015

Self-Financing Trading and the Ito-Doeblin Lemma

The objective of the note is to remind readers on how self-financing works in Quantitative Finance. The authors have observed continuing uncertainty on this issue which may be because it lies exactly at the intersection of stochastic calculus and finance. The concept of a self-financing trading strategy was originally, and carefully, introduced in (Harrison and Kreps 1979) and expanded very generally in (Harrison and Pliska 1981).

q-fin.PR↗

arXiv2015

Warehousing Credit (CVA) Risk, Capital (KVA) and Tax (TVA) Consequences

Credit risk may be warehoused by choice, or because of limited hedging possibilities. Credit risk warehousing increases capital requirements and leaves open risk. Open risk must be priced in the physical measure, rather than the risk neutral measure, and implies profits and losses. Furthermore the rate of return on capital that shareholders require must be paid from profits. Profits are taxable and losses provide tax credits. Here we extend the semi-replication approach of Burgard and Kjaer (2013) and the capital formalism (KVA) of Green, Kenyon, and Dennis (2014) to cover credit risk warehousing and tax, formalized as double-semi-replication and TVA (Tax Valuation Adjustment) to enable quantification.

q-fin.PR↗

arXiv2014

Efficient XVA Management: Pricing, Hedging, and Attribution using Trade-Level Regression and Global Conditioning

Banks must manage their trading books, not just value them. Pricing includes valuation adjustments collectively known as XVA (at least credit, funding, capital and tax), so management must also include XVA. In trading book management we focus on pricing, hedging, and allocation of prices or hedging costs to desks on an individual trade basis. We show how to combine three technical elements to radically simplify XVA management, both in terms of the calculations, and the implementation of the calculations. The three technical elements are: trade-level regression; analytic computation of sensitivities; and global conditioning. All three are required to obtain the radical efficiency gains and implementation simplification. Moreover, many of the calculations are inherently parallel and suitable for GPU implementation. The resulting methodology for XVA management is sufficiently general that we can cover pricing, first- and second-order sensitivities, and exact trade-level allocation of pricing and sensitivities within the same framework. Managing incremental changes to portfolios exactly is also radically simplified.

q-fin.CP↗

arXiv2014

KVA: Capital Valuation Adjustment

Credit (CVA), Debit (DVA) and Funding Valuation Adjustments (FVA) are now familiar valuation adjustments made to the value of a portfolio of derivatives to account for credit risks and funding costs. However, recent changes in the regulatory regime and the increases in regulatory capital requirements has led many banks to include the cost of capital in derivative pricing. This paper formalises the addition of cost of capital by extending the Burgard-Kjaer (2013) semi-replication approach to CVA and FVA to include an addition capital term, Capital Valuation Adjustment (KVA, i.e. Kapital Valuation Adjustment to distinguish from CVA.) The utilization of the capital for funding purposes is also considered. The use of the semi-replication approach means that the flexibility around the treatment of self-default is carried over into this analysis. The paper further considers the practical calculation of KVA with reference to the Basel II (BCBS-128) and Basel III (BCBS-189) capital regimes and their implementation via CRD IV. The paper also assesses how KVA may be hedged, given that any hedging transactions themselves lead to regulatory capital requirements and hence capital costs. Finally a number of numerical examples are presented to gauge the cost impact of KVA on vanilla derivative products.

q-fin.PR↗

arXiv2014

Regulatory-Optimal Funding

Funding is a cost to trading desks that they see as an input. Current FVA-related literature reflects this by also taking funding costs as an input, usually constant, and always risk-neutral. However, this funding curve is the output from a Treasury point of view. Treasury must consider Regulatory-required liquidity buffers, and both risk-neutral (Q) and physical measures (P). We describe the Treasury funding problem and optimize against both measures, using the Regulatory requirement as a constraint. We develop theoretically optimal strategies for Q and P, then demonstrate a combined approach in four markets (USD, JPY, EUR, GBP). Since we deal with physical measures we develop appropriate statistical tests, and demonstrate highly significant (p<0.00001), out-of-sample, improvements on hedged funding with a combined approach achieving 44% to 71% of a perfect information criterion. Thus regulatory liquidity requirements change both the funding problem and funding costs.

q-fin.PR↗