Credit valuation adjustment wrong-way risk modelling of foreign exchange sensitive derivatives
Salonen, Tommi (2023)
Salonen, Tommi
2023
Tuotantotalouden DI-ohjelma - Master's Programme in Industrial Engineering and Management
Johtamisen ja talouden tiedekunta - Faculty of Management and Business
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Hyväksymispäivämäärä
2023-10-10
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:tuni-202309238398
https://urn.fi/URN:NBN:fi:tuni-202309238398
Tiivistelmä
In derivatives pricing credit valuation adjustment (CVA) is used to quantify the counterparty credit risk. Wrong-way risk refers to possibility that the counterparty's insolvency probability is increasing at the same time as the value of the contract increases. The methods used to model CVA often assume that probability of default and exposure are independent of each other, and thus the wrong-way risk is not considered. However, market crises, for example the eurozone debt crisis of 2010, have shown that the assumption of market-credit independence is often violated. The observation is supported by empirical studies, both on historical data and market-implied data. The market is pricing wrong-way risk, which can be seen, for example, in the spreads of credit default swaps quoted in different currencies referring to same entity. The regulator also recognizes the existence of wrong-way risk and requires measures to monitor and manage it.
In this thesis CVA wrong-way risk modelling is studied in the case of a cross-currency basis swap and a systemically significant counterparty. By nature, wrong-way risk is portfolio-specific and difficult to model, and as the topic of WWR is relatively new, there are no established practices. The goals of this thesis are:
(i) Identify methods of modelling credit value adjustment wrong-way risk of derivatives contract having foreign exchange risk factor.
(ii) Model CVA WWR in realistic market setting with an example contract where bilateral collateral is posted and compare results with simple CVA model where WWR is ignored.
Two methods were selected for wrong-way risk modeling, one of which is based on a constant correlation of the error components of the models used for stochastic modeling of the exchange rate and default probability, and the other on the relative, instant jump of the exchange rate at the time of default of the counterparty. A joint model of these methods is derived, which is examined in the empirical part of the work from the point of view of a cross-currency basis swap. A sensitivity analysis is performed with key parameters of the methods.
Based on the results of the empirical part, the constant correlation method is not producing a significant wrong-way risk effect in the case of the modelled contract when collateral is used. Instead, the assumed relative jump in the exchange rate at the time of default of the counterparty causes a significant relative change in the value of the CVA compared to the model without wrong-way risk. The effect is particularly large in the case of a collateralized contract, as the lagged collateral is not able to reduce the jump-at-default effect. The results are in line with previous literature: linear correlation alone does not cause a significant wrong-way risk to the collateralized portfolio but jump-at-default can be a significant source of additional risk. In managerial decisions the possibility of jump-at-default should not be ignored.
In this thesis CVA wrong-way risk modelling is studied in the case of a cross-currency basis swap and a systemically significant counterparty. By nature, wrong-way risk is portfolio-specific and difficult to model, and as the topic of WWR is relatively new, there are no established practices. The goals of this thesis are:
(i) Identify methods of modelling credit value adjustment wrong-way risk of derivatives contract having foreign exchange risk factor.
(ii) Model CVA WWR in realistic market setting with an example contract where bilateral collateral is posted and compare results with simple CVA model where WWR is ignored.
Two methods were selected for wrong-way risk modeling, one of which is based on a constant correlation of the error components of the models used for stochastic modeling of the exchange rate and default probability, and the other on the relative, instant jump of the exchange rate at the time of default of the counterparty. A joint model of these methods is derived, which is examined in the empirical part of the work from the point of view of a cross-currency basis swap. A sensitivity analysis is performed with key parameters of the methods.
Based on the results of the empirical part, the constant correlation method is not producing a significant wrong-way risk effect in the case of the modelled contract when collateral is used. Instead, the assumed relative jump in the exchange rate at the time of default of the counterparty causes a significant relative change in the value of the CVA compared to the model without wrong-way risk. The effect is particularly large in the case of a collateralized contract, as the lagged collateral is not able to reduce the jump-at-default effect. The results are in line with previous literature: linear correlation alone does not cause a significant wrong-way risk to the collateralized portfolio but jump-at-default can be a significant source of additional risk. In managerial decisions the possibility of jump-at-default should not be ignored.