Credit Risk of Derivatives

Derivatives also have credit risk, and incorporating that risk into their price is relatively more difficult than in the case of stocks or bonds.

When options or futures are traded through trading platforms, people think less about credit risk, because clearinghouses neutralize much of that risk by requiring appropriate margins. But in the pricing of OTC — Over-The-Counter — derivatives, credit risk can have a significant impact.

There can be three types of contracts:
– A contract that is always a liability for us — Short Option.
– A contract that is always an asset for us — Long Option.
– A contract that can sometimes be an asset and sometimes a liability — Forward.

In the case of a short position, for example when you have sold an option, counterparty credit risk does not affect you in the same way. If the other side defaults, you do not lose anything from that default.

In the case of a long contract, your credit risk does exist, and it depends on:

1. The positive value of the contract — Exposure
2. The probability of default
3. The recovery rate

A rough example:
If, in the absence of credit risk, an option would be worth $100, and the probability of default is 5%, while the expected recovery rate in case of default is 40%, then the expected loss would be:

100 × 5% × (1 − 40%) = $3

So the risk-adjusted value of the option would be $97.

In the case of a forward contract, the calculation becomes more complicated, because before maturity, gains and losses can replace each other many times.
This is where the term CVA — Credit Value Adjustment — appears.
Conceptually, CVA represents the present value, discounted at the risk-free rate, of the expected loss caused by the counterparty’s default.

CVA = Σ [Default Probability × Loss Given Default × Present Value of Expected Exposure]

Or:

CVA = Σ qᵢ × (1 − R) × vᵢ

Symbol	Meaning
qᵢ	Risk-neutral probability of default at time i
R	Recovery rate
1 − R	Loss given default
vᵢ	Present value of exposure at time i

The value of such derivatives can also be estimated using a market-based method.

For example, suppose we have a two-year contract that would be worth $3 without default risk, and the counterparty’s credit spread above the risk-free rate is 1.5%. In that case, we can discount it to arrive at the value of the risky derivative:

3 × e^(−1.5% × 2) = 2.91

This approach works especially well when the derivative is always an asset for us. In forward/swap-type contracts, where the value can be positive at one point and negative at another, a more detailed CVA approach is required.

P.S.
There is also a distinction between Wrong-Way Risk and Right-Way Risk.
In the examples above, the assumption is that the positive value of the contract — Exposure — is not correlated with the probability of default. But in some cases, this is not true.

For example, suppose a bank enters into a forward contract with a fuel supplier, in such a way that a decline in oil prices is profitable for the bank, and the opposite is unfavorable.

In that case, the development of events in favor of the bank’s profitability would be directly correlated with an increase in the counterparty’s default risk.
This would be a contract carrying Wrong-Way Risk.

P.P.S.
Understanding credit risk in derivatives is important beyond the financial world as well — especially when dealing with real options and forward-type contractual agreements.

Source:
Options, Futures and Other Derivatives — John C. Hull.