The price that an investor would pay to hedge the counterparty credit risk of a derivative instrument

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## What is Credit Valuation Adjustment (CVA)?

Credit Valuation Adjustment (CVA) is the price that an investor would pay to hedge the counterparty credit risk of a derivative instrument. It reduces the mark to market value of an asset by the value of the CVA.

Credit Valuation Adjustment was introduced as a new requirement for fair value accounting during the 2007/08 Global Financial Crisis. Since its introduction, it has attracted dozens of derivatives market participants, and most of them have incorporated CVA in deal pricing.

### Formula for Calculating Credit Valuation Adjustment

The formula for calculating CVA is written as follows:

Where:

• T = Maturity period of the longest transaction
• Bt = Future value of one unit of the base currency invested at the current interest rate at T maturity
• R = Fraction of the portfolio value that can be removed in case of default
• T = Time of default
• dPD(0,t)= Risk-neutral probability of counterparty default (between times s and t)
• E(t) = Exposure at time T

### History of Credit Valuation Adjustment

The concept of credit risk management, which includes credit valuation adjustment, was developed due to the increased number of country and corporate defaults and financial fallouts. In recent times, there have been cases of sovereign entity defaults, such as Argentina (2001) and Russia (1998). At the same time, a high number of large companies collapsed before, during, and after the financial crisis of 2007/08, including WorldCom, Lehman Brothers, and Enron.

Initially, research in credit risk focused on the identification of such a risk. Specifically, the focus was on counterparty credit risk, which refers to the risk that a counterparty may default on its financial obligations.

Prior to the 2008 financial crisis, market participants treated large derivative counterparties as too big to fail and, therefore, never considered their counterparty credit risk. The risk was often ignored due to the high credit rating of counterparties and the small size of derivative exposures. The assumption was that the counterparties could not default on their financial obligations like other parties.

However, during the 2008 financial crisis, the market experienced dozens of corporate collapses, including large derivative counterparties. As a result, market participants started incorporating credit valuation adjustment when calculating the value of over-the-counter derivative instruments.

### Challenges to Counterparty Credit Risk

Derivative instruments can be classified as either unilateral or bilateral, depending on the nature of the payoff.

#### 1. Unilateral derivate instruments

For a unilateral derivative instrument holder, exposure to loss occurs if a counterparty defaults on their financial obligations. The amount of loss that an investor incurs is equal to the fair value of the instrument at the time of default.

#### 2. Bilateral derivative instruments

Bilateral derivatives are more complex than unilateral derivatives, since the former includes two-way counterparty risk. This means that both the counterparty and the investor are exposed to counterparty risk. The advantage of bilateral derivatives is that the derivative may adopt an asset or liability position at any valuation date.

For example, if Counterparty A is at a positive asset position today, it is exposed to Counterparty B. If A defaults on his obligation, he will owe the positive asset to B. The same applies if B is in a negative liability position because, in case of default, he owes the negative liability position to A.

### CVA Valuation Methods

There are several methods that are used to value derivatives, and they vary from simple to advanced methodologies. Determining the credit valuation adjustment method to use depends on the organization’s sophistication and resources available to the market participants.

#### 1. Simple approach

The simple method calculates the mark to market value of the instrument. The calculation is then repeated to adjust the discount rates by the counterparty’s credit spread. Calculate the difference between the two resulting values to obtain the credit valuation adjustment.

#### 2. Swaption-type valuation

The swaption-type is a more complex credit valuation adjustment methodology that requires advanced knowledge of derivative valuations and access to specific market data. It uses the counterparty credit spread to estimate the replacement value of the asset.

#### 3. Simulation modeling

This involves the simulation of market risk factors and risk factor scenarios. The derivatives are then revalued using multiple simulation scenarios. The expected exposure profile of each counterparty is determined by aggregating the resulting matrix. Each counterparty’s expected exposure profile is adjusted to derive the collateralized expected exposure profile.