Michael Brenndoerfer | Data & AI, Private Equity, Technology

Michael Brenndoerfer

Counterparty Risk and CVA › CVA Sensitivity Analysis

Michael BrenndoerferDecember 23, 20253 min read

Quantitative FinanceAll chapters

Part 10 of 15Risk Management and Financial Risk Controls

Chapter 56Counterparty Risk and CVA › CVA Sensitivity Analysis

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CVA is sensitive to three main drivers: credit quality (CDS spread), exposure profile (driven by market parameters), and recovery assumptions. Understanding these sensitivities is essential for risk management because they tell us which factors matter most for a given position and how CVA might change as market conditions evolve.

In[15]:

Code

import numpy as np

# Sensitivity to CDS spread
cds_spreads = np.linspace(0.005, 0.05, 20)  # 50 to 500 bps
cvas_by_spread = []

for spread in cds_spreads:
    mpd, _ = calculate_default_probabilities(spread, recovery_rate, times)
    cva_temp = calculate_cva(expected_exposure, mpd, discount_factors, lgd)
    cvas_by_spread.append(cva_temp)

# Sensitivity to recovery rate
recovery_rates = np.linspace(0.2, 0.6, 20)
cvas_by_recovery = []

for rec in recovery_rates:
    lgd_temp = 1 - rec
    mpd, _ = calculate_default_probabilities(cds_spread, rec, times)
    cva_temp = calculate_cva(expected_exposure, mpd, discount_factors, lgd_temp)
    cvas_by_recovery.append(cva_temp)

Out[16]:

Visualization

Upward, nearly linear curve of CVA from about 1.2 thousand dollars at a 50 basis-point CDS spread to about 10 thousand dollars at 500 basis points. — CVA sensitivity to counterparty CDS spread. The relationship is near-linear for moderate spread levels, as default probability scales proportionally with credit spreads.

Gently downward-curving CVA sensitivity from about 3.62 thousand dollars at 20 percent recovery to about 3.41 thousand dollars at 60 percent recovery. — CVA sensitivity to recovery rate. The total adjustment decreases as recovery increases, showing the inverse relationship between recovery and the loss given default component of CVA.

The near-linear relationship between CVA and CDS spread reflects the first-order approximation in the CVA formula. Since default probability is approximately proportional to the hazard rate, and the hazard rate is proportional to the CDS spread, CVA increases roughly linearly with spread. This relationship is extremely useful for hedging, as it suggests that a simple CDS position can offset most of the credit spread risk in CVA.

The recovery rate sensitivity shows a less intuitive pattern: while higher recovery reduces LGD, it also implies lower hazard rates for the same CDS spread, creating offsetting effects. When recovery is high, each default is less costly (lower LGD), but the implied hazard rate from the CDS market is also higher (since the same spread must compensate for smaller expected losses per default, there must be more defaults). These two effects partially cancel, making CVA less sensitive to recovery assumptions than one might initially expect.