BR-CVA with Wrong Way Risk and SABR Hedging for FX Option

Bilateral Counterparty Risk Valuation Adjustment with Wrong Way Risk on Collateralized Commodity Counterparty: Basel III explicitly requires banks to include credit value adjustment (CVA) into capital charges, and both CVA and debt value adjustment (DVA) are required to be included in the accounting value for derivatives that are using market-to-market accounting rule. Wrong-way risk (WWR) refers to when the counterparty credit exposure increases as the default probability increases. WWR can significantly impact CVA and collateralized exposure. This paper proposes an effective method to calculate bilateral-CVA (BR-CVA) by incorporating WWR on a collateralized counterparty.  Unilateral CVA implicitly assumes that the institution making the computation will never default; in contrast, BR-CVA assumes both the institution and the counterparty can default, making the pricing more consistent with the financial institution’s risk management and accounting rule. BR-CVA is managed on the counterparty level because the netting and collateral agreement can significantly affect the counterparty credit exposure. This paper proposes a pricing framework of BR-CVA calculation on the counterparty level by considering a 2-way collateral agreement. The proposed method handles WWR by building a Gaussian copula between aggregate market risk exposure factor, and the default quality of the financial institution and counterparty. Conditional exposure can be calculated by leveraging the pre-computed exposure matrix together with the joint market-credit co-dependence structure. In the literature, either CVA with WWR and 1-way collateral agreement, or BR-CVA with 1-way WWR and without collateral have been studied. This paper extends the theoretical model, and links BR-CVA pricing, WWR and collateral modeling altogether. The WWR and collateral modeling are both bilaterally. The proposed model is close to the regulation requirement and practical to the financial institution’s risk management. A practical example is given in the end. Numerical results show the proposed methodology is efficient and robust: BR-CVA pricing dynamically depends on the underlying market risk factor, the credit quality of both parties, and 2-way collateral agreement. Moreover, the proposed method can easily stress test the impact of WWR in BR-CVA pricing. Both the direction and strength of WWR can be stress tested.

Sabr hedging for fx options: is it worth for the effort? This paper applies stochastic alpha-beta-rho (SABR) model to the foreign exchange (FX) market. The delta and vega hedging performance of the SABR model applied to FX vanilla options is evaluated, a topic never previously studied in the literature. After adapting the FX market-specific convention in volatility quotation, the SABR model is calibrated to fit the market’s implied smile. The model dynamics and hedging performance are then tested using historical data, the testing period and data description can b found in data section. Tests indicate that the SABR dynamic state variables — underlying FX forward and volatility of the FX forward— indeed account for the observed option price change. The hedging results indicate that the SABR model provides a more accurate hedge ratio than BS (Black-Sholes) model does.