Cutting Edge: the year of CVA

The year of CVA

With derivatives counterparty risk rocketing up the agenda this year, researchers have tried to shed some light on the associated challenges - from capital calculation to pricing - as the annual round-up of Risk's technical papers and citations shows. By Laurie Carver

Who says quants occupy an ivory tower? This year’s technical articles reflect a preoccupation with a real-world concern – credit value adjustment (CVA), or the counterparty credit component of derivatives market value. Six of the 26 articles published by Risk in the past 12 months focused on the topic, which has shot to prominence as a result of the credit stress many banks are suffering, and the punitive capital charge that will be levied against CVA when portions of Basel III are implemented in 2013.

Researchers showed a commendable willingness to get their hands dirty, tackling issues of practical value for dealers, end-users and regulators. Michael Pykhtin, a quant at the Federal Reserve Board in Washington, was critical of aspects of the Basel approach in Counterparty risk capital and CVA, which described the capital formula as inaccurate and proposed an alternative (Risk August 2011, pages 66–71). Pykhtin also called for regulators to let banks model CVA and allow market risk offsets, warning that not doing so could lead to perverse outcomes, as hedges are currently treated by the rules as stand-alone positions.

One difficult aspect of CVA is wrong-way risk – put simply, situations in which exposure is positively correlated with default risk. Capturing credit correlation between counterparty and underlying, by Kirk Buckley, Sascha Wilkens and Vladimir Chorniy of BNP Paribas, used Robert Merton’s classic credit model in a counterparty context to get a handle on wrong-way risk for large portfolios (Risk April 2011 pages 66–70).

But possibly the most challenging part of CVA implementation is its numerical complexity. The adjustment for a given netting set is simply the expected loss on the portfolio, but the exposures can be across many different asset classes, involving many embedded options with complicated exercise rights – so the result is a complex hybrid derivative, the sensitivities of which are difficult to calculate.

Real-time counterparty credit risk management in Monte Carlo (Risk June 2011, pages 82–86), by a team at Credit Suisse led by Luca Capriotti, showed how to simplify the task of finding sensitivities using a mathematical trick called ‘adjoint differentiation’, which reverses the order of certain operations in the calculation.

If that’s the most challenging element of CVA, then its twin, the debit value adjustment (DVA) – which reflects market value shifts resulting from changes in a dealer’s own creditworthiness – is perhaps the most talked-about. DVA became particularly controversial following the publication of third-quarter results, when first UBS, then JP Morgan, Bank of America Merrill Lynch and Morgan Stanley all reported large gains as a result of DVA – essentially booking an upfront profit from the worsening of their credit. Goldman Sachs threw many commentators by implementing a DVA hedging programme – buying back its own debt, or instruments correlated with it, to offset what otherwise would have been similarly large gains.

This kind of hedging programme was explored by Massimo Morini and Andrea Prampolini in Risky funding with counterparty and liquidity charges, where they showed that the bond-credit default swap (CDS) basis – rather than simply the CDS spread – was the key to understanding the effect of hedging strategies on the balance sheet (Risk March 2011, pages 70–75).

November saw a CVA double bill as Solum Financial’s Jon Gregory and Frederic Vrins of ING Bank showed in Getting CVA up and running how to convert the normally upfront premium into a rolling spread that could be more palatable to end-users (Risk November 2011, pages 76–79). The month’s other article saw Christoph Burgard and Mats Kjaer of Barclays Capital expand on Morini and Prampolini’s ideas using Merton’s classic replication argument to derive a partial differential equation analogous to the Black-Scholes pricing equation to describe the economic value of a derivative to a dealer, given the funding costs associated with the CVA and DVA adjustments (Risk November 2011, pages 72–75).

But this was far from the only subject on quants’ minds. Three pivotal articles on the calibration of implied volatility surfaces showed that even in areas previously thought simple, important problems remain, and can be solved. In the first of their two contributions, Danske Bank’s Jesper Andreasen and Brian Huge developed a method for interpolating implied volatilities across strikes – they would later incorporate this into a radical rethinking of the calibration problem in the second, Random grids (Risk March 2011, pages 76–79, Risk July 2011, pages 62–67).

This article ditched the continuous time model as the basic calibration template, replacing it with a discretised version with an embedded transition matrix for Monte Carlo compatibility and using Andreasen and Huge’s previous interpolation scheme to sweep across strikes at each step. The result is a dramatic reduction in computation time, and a smoother calibration of implied volatility surfaces.

This work was later built on by Alex Lipton and Artur Sepp of Bank of America Merrill Lynch (BAML) in Filling the gaps, which incorporates the classical Laplace transform to convert the scheme being solved by Andreasen and Huge into a more manageable form, and then proceeding in a similar numerical fashion (Risk October 2011, pages 78–83).

The focus on volatility and counterparty risk this year is reflected in the ranking of authors by their citations in other Risk articles (see table A, which counts at most two citations per author in each citing article - all tables can be found by following the link at the foot of this article): Andreasen and Huge are joined by Bloomberg’s Bruno Dupire and BAML’s Lipton in volatility research, with Gregory and Brigo most prominent in the field of counterparty risk. Barclays Capital’s Vladimir Piterbarg tops the list, primarily due to his seminal article on risk-neutral valuation of collateralised trades (Risk February 2010, pages 97–102).

Volatility has a lasting fascination for researchers, of course, as demonstrated by the classic paper from the University of Maryland’s Steven Heston – it was the first to look at explicitly modelling the stochastic dynamics of volatility, and this year draws level with Merton’s credit risk paper in terms of citations in Risk articles over the past 10 years (see table D). Pricing with a smile, by Bloomberg’s Dupire, remains the most-cited article originally published in Risk (Risk July 1994, pages 18–20).

Risk’s most published author, Richard Martin of Man Investments, took his total to 16 with Mean reversion pays, but costs, co-written with his colleague Torsten Schöneborn (Risk February 2011, pages 84–89).

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