Abstract
This dissertation addresses the significant influence ofWWR(WWR) on Credit Valuation
Adjustment (CVA) calculations, a component often overlooked in CVA due to its computational
and tractability challenges. We present a comparative analysis by modeling CVA
with and without WWR and demonstrate its impact, particularly when using two WWRinclusive
approaches. The first approach we explore is the Hull and White model, which
integrates WWR by adjusting the hazard function to account for the value of the derivative
with the counterparty. This aims to provide a more accurate capture of counterparty risk.
The second approach, proposed by Cherubini, models WWR using copulas to model the
dependencies between default events and exposures.
We also model CVA with two distinct default probability measures, namely, the risk-neutral
default probability and the real-world default probability measure. The risk-neutral default
probability measure is derived from market credit spreads to reflect future expectations,
where the real-world default probabilities are based on historical data, with two variations,
namely, one derived from historical default events and credit ratings and another using the
Merton model, which uses equity data to estimate default likelihoods. Using an interest rate
swap as our underlying which we simulate using the Vaˇsi ˇ cek short rate model, our analysis
compares these approaches to highlight the impact of WWR on CVA values.
In particular, our simulation results show that omitting WWR typically leads to underestimation
of CVA values across all default probability types. In contrast, both WWR-inclusive
methods yield substantially higher CVA values, underscoring the necessity of incorporating
WWR in CVA calculations for more accurate counterparty risk assessments.