Credit valuation adjustment (CVA) is the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. In other words, CVA is the market value of counterparty credit risk. This price depends on counterparty credit spreads as well as on the market risk factors that drive derivatives’ values and, therefore, exposure. Various related adjustments, collectively xVA, are discussed under Financial economics#Extensions.
Contents
- Exposure independent of counterparty default
- Approximation
- Function of the CVA desk and implications for technology
- References
Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation can be written as
where
More generally CVA can refer to a few different concepts:
According to the Basel Committee on Banking Supervision's July 2015 consultation document regarding CVA calculations, if CVA is calculated using 100 timesteps with 10,000 scenarios per timestep, 1 million simulations are required to compute the value of CVA. Calculating CVA risk would require 250 daily market risk scenarios over the 12-month stress period. CVA has to be calculated for each market risk scenario, resulting in 250 million simulations. These calculations have to be repeated across 6 risk types and 5 liquidity horizons, resulting in potentially 8.75 billion simulations.
Exposure, independent of counterparty default
Assuming independence between exposure and counterparty’s credit quality greatly simplifies the analysis. Under this assumption this simplifies to
where
Approximation
Full calculation of CVA is done via Monte-Carlo simulation of all risk factors which is very computationally demanding.There exists a simple approximation for CVA which consists in buying just one default protection (Credit Default Swap) for amount of NPV of netted set of derivatives for each counterparty.[2]
Function of the CVA desk and implications for technology
In the view of leading investment banks, CVA is essentially an activity carried out by both finance and a trading desk in the Front Office. Tier 1 banks either already generate counterparty EPE and ENE (expected positive/negative exposure) under the ownership of the CVA desk (although this often has another name) or plan to do so. Whilst a CVA platform is based on an exposure measurement platform, the requirements of an active CVA desk differ from those of a Risk Control group and it is not uncommon to see institutions use different systems for risk exposure management on one hand and CVA pricing and hedging on the other.
A good introduction can be found in a paper by Michael Pykhtin and Steven Zhu. Karlsson et al. (2016) present a numerical efficient method for calculating expected exposure, potential future exposure and CVA for interest rate derivatives, in particular Bermudan swaptions.