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

## 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 united 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 was developed due to the increased number of country and corporate defaults and financial fallouts. In recent times, there have been cases of sovereign entities defaults such as the case of Argentina (2001) and Russia (1998). At the same time, there has been a high number of large companies collapse before 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 occurs when a counterparty defaults on its financial obligations.

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 the derivative exposures. The assumption was that the counterparties could not default on their financial obligations like other parties.

However, during the financial crisis of 2007/2008, the market experienced dozens of corporate collapses, including large derivative counterparties. As a result, market participants started incorporating the value of counterparty credit risks 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, the exposure to loss would occur if the counterparties were to default 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.

Since a derivative is a contract between two counterparties, the obligation and risk exposure resulting from selling the option to an investor remains constant, regardless of whether the investor defaults. In the event of default by the investor, the money owed by the counterparty to the investor would remain.

#### 2. Bilateral derivative instruments

On the other hand, bilateral derivatives are more advanced than unilateral derivatives, since the former includes a two-way counterparty risk. It means that both the counterparty and the investor are exposed to each other. The limitation with 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 CVA valuation method to use depends on the organization’s sophistication and resource 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 CVA valuation 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

It involves the simulation of market risk factors and risk factor scenarios. The derivatives are then revalued using multiple simulation scenarios by time steps. 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.

### More Resources

CFI offers the Financial Modeling & Valuation Analyst (FMVA)™ certification program for those looking to take their careers to the next level. To keep learning and advancing your career, the following resources will be helpful:

• Basis Risk
• Credit Default Swap (CDS)
• Hedging Arrangement
• Options: Calls and Puts

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