The conference is going to take place at Eötvös Loránd University, Budapest, Hungary Pázmány Péter Sétány 1/A, Gömb Aula.
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The market for financial products and derivatives reached an outstanding notional size of 708 USD Trillions in 2011, amounting to ten times the planet gross domestic product. Even discounting double counting, derivatives appear to be an important part of the world economy and have played a key role in the onset of the financial crisis in 2007. We describe the changes triggered by post 2007 events on the theory of valuation. We re-discuss the valuation theory assumptions and introduce consistent valuation under counterparty credit risk, collateral posting, initial and variation margins, funding costs and capital costs. We explain model dependence induced by credit effects, hybrid features, contagion, payout uncertainty, and nonlinear effects due to replacement closeout at default and possibly asymmetric borrowing and lending rates in the margin interest and in the funding strategy for the hedge of the relevant portfolio. Nonlinearity manifests itself in the valuation equations taking the form of semi-linear PDEs or Backward SDEs. We present an invariance theorem showing that the final valuation equations do not depend on unobservable risk free rates, that become purely instrumental variables. Valuation is thus based only on real market rates and processes. We also present a high level analysis of the consequences of nonlinearities, both from the point of view of methodology and from an operational angle, including deal/entity/aggregation dependent valuation probability measures and the role of banks treasuries. We briefly discuss conditions under which adjustments can be disentangled. Finally, we hint at how one may connect these developments to interest rate theory under multiple discount curves and to valuations for CCP cleared trades, thus building a consistent valuation framework encompassing most post-2007 effects.
Wolfgang Wimmer from Erste Group will give an overview about the current challenges in the counterparty credit risk area. The presentation will show how different risk measures for OTC derivatives are used in the daily monitoring process and it will explain how the arising credit risk can be mitigated. Furthermore the course will conclude with an outlook on regulatory changes related to counterparty credit risk (SA-CCR and CVA).
In the aftermath of the financial crisis, regulators launched in a major effort of banking reform aimed at securing the financial system by raising collateralisation and capital requirements. Notwithstanding finance theories according to which costs of capital and of funding for collateral are irrelevant to decisions, banks have introduced an array of XVA metrics to precisely quantify them. In particular, KVA (capital valuation adjustment) and FVA (funding valuation adjustment) are emerging as metrics of key relevance.
We introduce a capital structure model acknowledging the impossibility for a bank to hedge jump-to-default related cash flows. Because of this counterparty credit risk incompleteness, deals trigger wealth transfers from bank shareholders to bank creditors and shareholders need to set capital at risk. On this basis we obtain a theory of XVAs where so-called contra-liabilities and cost of capital are sourced from bank clients at trade inceptions, on top of the fair valuation of counterparty credit risk, in order to compensate shareholders for wealth transfers and risk on capital.
We introduce a framework for assessing KVA, reflect it into entry prices and distribute it gradually to the bank shareholders through a dividend policy that would be sustainable even in the limit case of a portfolio held on a run-off basis, with no new trades ever entered in the future. Our FVA is defined asymmetrically since there is no benefit in holding excess capital in the future. We notice that capital is fungible as a source of funding for variation margin (but not for initial margin), causing a material reduction in the FVA numbers.
In this research, we investigate the impact of stochastic volatility and interest rates on counterparty credit risk (CCR) for FX derivatives. To achieve this we analyse two real-life cases in which the market conditions are different, namely during the 2008 credit crisis where risks are high and a period after the crisis in 2014, where volatility levels are low. The Heston model is extended by adding two Hull–White components which are calibrated to fit the EURUSD volatility surfaces. We then present future exposure profiles and credit value adjustments (CVAs) for plain vanilla cross-currency swaps (CCYS), barrier and American options and compare the different results when Heston–Hull–White or Black–Scholes dynamics are assumed. It is observed that the stochastic volatility has a significant impact on all the derivatives. For CCYS, some of the impact can be reduced by allowing for time-dependent variance. We further confirmed that Barrier options exposure and CVA is highly sensitive to volatility dynamics and that American options’ risk dynamics are significantly affected by the uncertainty in the interest rates.
The Longstaff–Schwartz method (LSM) is an industry standard for valuing American/Bermudan-style options. In this talk we briefly summarize the theoretical background and show how the LSM approach can be used for expected exposure calculations with a focus on the practical implementation in the XVA framework.
The focus of this research is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of paths for nested Monte Carlo simulations, resulting in large variances of estimators in practice. We propose a novel approach based on Kolmogorov forward and backward PDEs, where we counter the high dimensionality by a generalisation of anchored-ANOVA decompositions. By computing only the most significant term in the decomposition, the dimensionality is reduced effectively, such that a significant computational speed-up arises from the high accuracy of PDE schemes in low dimensions compared to Monte Carlo estimation. Moreover, we show how this truncated decomposition can be used as control variate for the full high-dimensional model, such that any approximation errors can be corrected while a substantial variance reduction is achieved compared to the standard simulation approach. We investigate the accuracy for a realistic portfolio of exchange options, interest rate and cross-currency swaps under a fully calibrated seven-factor model.
CVA, FVA, DVA (credit valuation adjustment, funding valuation adjustment, debit valuation adjustment; they are also referred to as ‘XVA’) are hot topics in contemporary finance and derivatives pricing. We will give a short overview of the topic and present a framework to take all these costs and risks into consideration.
We will discuss a technique called the ‘funding invariance principle’ to show that, interestingly, as long as funding cash-flows are included in the valuation of a financial contract, the choice of the discounting rate is irrelevant.
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The workshop is also supported by the Pallas Athéné Domus Scientiae Foundation.
Counterparty exposure has become the key element of financial risk management, highlighted by the bankruptcy of the investment bank Lehman Brothers and failure of other high profile institutions such as Bear Sterns, AIG, Fannie Mae and Freddie Mac.
Unlike the credit risk for a loan, when only the lending banking organization faces the risk of loss, counterparty exposure creates a bilateral risk of loss. The future market value of the exposure and the counterparty’s credit quality are uncertain and may vary over time as underlying market factors change. Standard credit risk models cannot explain the observed clustering of default, sometimes described as “credit contagion”. Counterparty risk is a potential channel of credit contagion, and its modelling needs complex approaches. Regulators try to mitigate counterparty risk by increasing capital reserve requirements. A more market-conform solution is Credit Valuation Adjustments, when the price an investor requires for a product is reduced in the trade with a default-risky counterparty as opposed to a default free one. However, various approaches, going beyond CVA also appear in the literature, but they slowly gain acceptance in the financial industry.
The pricing and management of counterparty credit and funding risk is a very complex, model-dependent task and requires a holistic approach to modelling that goes against much of the ingrained culture in most of the financial industry and regulators, and even of most traditional western science to some extent. Regulators and part of the industry are desperately trying to standardize the related calculations in the simplest possible ways but our conclusion will be that such effects are complex and need to remain so to be properly accounted for. The attempt to standardize every risk to simple formulas is misleading and may result in the relevant risks not being addressed at all. Instead, industry and regulators should acknowledge the complexity of this problem and work to attain the necessary methodological and technological prowess to handle it, rather than trying to bypass it.