# Credit Risk Charges in Derivatives Pricing

*Bankruptcy isn’t pretty, even if it occurs to other organisations. If these organisations are your trading partners, you risk losing out on lucrative deals. This is why banks charge a credit risk spread if you conclude an uncollateralised derivative. How is such a spread calculated and how does it impact the price of the derivative?*

In the over-the-counter (OTC) derivatives market a distinction is made between collateralised derivatives and uncollateralised derivatives. A collateralised derivative is a derivative where the credit risk is managed via the exchange of collateral. In case the mark-to-market is moving positive from the bank’s perspective (profit position for the bank and a loss position for the client), the bank runs the risk that the profit will not be settled in their books if the counterpart goes bankrupt. The opposite is true in case the mark-to-market is moving negative from the bank’s perspective (loss position for the bank and a profit position for the client). In that case the client has the mark-to-market as a credit risk on the bank. In case of a collateralised derivative, the mark-to-market is exchanged between the two counterparties to manage this credit risk. How this collateral is exchanged is described in the so called credit support annex (CSA) between the bank and the client.

In case a derivative is traded and no collateral is exchanged, the derivative is called uncollateralised. In that case the bank will quantify the credit risk they have on the client, and this credit risk is charged in the pricing of the derivative (this is referred to as the credit value adjustment charge, or CVA). The client runs the same risk because the mark-to-market can also move in favour for the client, but this is not a concern for the bank (from the bank’s perspective, this is called the debit value adjustment, or DVA). Banks are mysterious about how they price this CVA charge. These charges can be significant; they depend on a number of variables such as the type of the transaction, the term of the transaction, the volatility of the underlying, and, most importantly, the so called probability of default of the client. This has an economic impact, but also external stakeholders require reporting of the fair value and the CVA and DVA of the derivative. It is not advisable to use the calculation of the bank because they are counterpart in the transaction. These calculations should be made independently so that unrightfully profits, made by the bank at conclusion of the contract, can be brought to the surface.

In order to create transparency in this world, an online Credit Risk Analyser has been made available.

**Measuring Credit Risk**

Credit risk can be measured in different ways. The most intuitive is the probability of default (POD) mentioned earlier. A POD of 5% at 4 years means there is a 5% chance the organisation defaults between now and four years from now. Unfortunately, this figure is hard to measure: at best, it’s an educated guess.

Another useful quantity is the rate at which the company can get loans or issue tradable debt. The higher the risk, the higher the rate. This relationship can be expressed mathematically.

A third possibility is the credit default swap (CDS) spread. A CDS is, in essence, an insurance against the default of a company. Its price is expressed as a spread, again higher for riskier companies.

**Credit Risk Analyser**

The Credit Risk Analyser is an interesting feature for the credit risk management on financial counterparties, but it can also be used for general business counterparties. The tool makes a quantitative analysis of the credit risk on a counterpart by calculating the credit default swap (CDS) and the probability of default of the counterpart. The CDS can also be calculated for non-exchange-listed counterparts.

The tool uses the credit risk analysis that funding suppliers (banks, public debt suppliers, leasing suppliers, etc) have made while calculating a funding proposal and / or by analysing tradable debt, such as bonds, medium term notes and commercial paper. The tool supplies an interesting add-on to traditional methods of quantifying the credit risk on counterparts. The calculated CDS levels can be used to create your own internal classification of credit risks on counterparts.

The tool can also analyse how the credit risk is priced in funding proposals that you receive (what probability of default is the bank pricing in the funding proposal, or, what should be the interest rate, given a certain probability of default). In this way the tool also supplies an analysis of the reasonability of the interest charged in funding proposals you receive. In case of tradable debt, the tool can analyse how the market as a whole is pricing the credit risk on your organisation.

**Pricing Uncollateralised Derivatives**

The Treasury Toolbox contains three pricers allowing you to calculate the value, cash flows and other relevant quantities for caps, floors, swaps and swaptions. Together with the Credit Risk Analyser, two new features are added to these pricers.

First, you can choose between a collateralised and an uncollateralised derivative. Even without taking into account credit risk, the exchange of collateral has an influence on the value of a derivative. Namely, an uncollateralised derivative runs a reinvestment risk, which needs to be taken into account. This feature is available independent of the Credit Risk Analyser.

Secondly, you can select any of your companies and any of the other companies stored within the Credit Risk Analyser as counterparts. If you do, and in the case of a cap, floor, swap or swaption, the CVA and DVA is calculated as well as the usual output of the pricer.

The Treasury Toolbox calculates the CVA and the DVA for uncollateralised derivatives without creating the need to input CDS data from market data vendors, which is not only expensive, but also burdensome because of the large number of counterparts an organisation can have. Also, with market data vendors CDS data can only be obtained for exchange listed counterparts, but not all counterparts are listed on an exchange.