Modern advances in computational credit risk modelling Quantitative approaches to margin value adjustments for interest rate derivatives

In an ongoing effort to reduce counterparty credit risk in the over-the-counter derivatives market, regulators have introduced a global policy framework for collateral requirements. A key form of collateral is Initial Margin (IM), which, unlike other types of collateral, cannot be rehypothecated and must be funded by the trading parties. The expected funding cost associated with posting IM over the lifetime of a trade is known as Margin Value Adjustment (MVA). The calculation of MVA depends on dynamic IM modeling and requires the simulation of future trade sensitivities, which presents a significant computational challenge.
This thesis approaches the problem from two angles: the numerical methodology and the analysis of model-risk. The numerical challenge is addressed by proposing a static replication algorithm for callable interest rate derivatives. Under appropriate modeling conditions, an equivalent portfolio of European options can be composed to replicate the value of these products. This replication allows the use of closed-form expressions to calculate conditional prices and sensitivities, greatly enhancing the efficiency of MVA computations.
The model-risk is analyzed by investigating the impact of volatility modeling on IM simulations. The Cheyette short-rate model is extended with a stochastic volatility component and calibrated to real market data. A comparative analysis shows that incorporating stochastic volatility can significantly affect expected collateral requirements for non-linear interest rate derivatives, especially when the market exhibits a pronounced smile or skew in the implied volatility curve.