The way I was taught is as follows:
Inherent risk = the risk a transaction or account has an error in it. Typically this risk is associated with the type of transaction or type of account in question. For example, when you are looking at a cash balance, it has a low inherent risk. Five $100 bills will always equal a balance of $500. There is no risk that five $100 bill will suddenly equate to a balance of $400 or $600.
On the other hand, stock options would have a higher inherent risk. There is a large degree of estimate and judgment that goes into valuing the options, especially if they are not traded on an active market. I might think the options are worth $500 and you might think they are worth $1,000. It's not so black and white. So it has a higher inherent risk of misstatement.
Control risk = The risk a misstatement will not be caught by controls. For example if you have new, uneducated employees who are in charge of overseeing transactions/accounts, they is a higher control risk than if you have well educated, experienced employees overseeing the same transactions/accounts. You are more likely to catch in error in the latter situation.
Detection risk = The risk a misstatement will not be caught by the auditor. For example, if an auditor sampled 100 of 1,000 accounts, there would be a higher detection risk than if the auditor sampled 900 of the 1,000 accounts.
Audit risk is the risk that a material misstatement will exists in the financial statements. It is equal to the product of control risk, detection risk, and inherent risk.
For example, if you were dealing with risky transactions with a high degree of inherent risk (let's say 50% for argument sake), and no controls were in place (a 100% control risk), but the auditor did substantive testing on ALL transactions, (i.e., there was no chance they would miss detecting the error and thus a 0% detection risk), then the audit risk would be 0%
50% x 100% x 0% = 0%
Now, to get to your specific example…
1) Derivative have a high inherent risk (there is a good chance they will be misvalued), so inherent risk would go up. More skilled employees would likely mean there is a better chance they would recognize an error in a derivative transaction, and thus control risk would go down (less chance a misstatement will go undetected). Detection risk likely would not change as that has to do with the auditor.
2) I don't quite understand what you're describing in the second transaction, but I'm guessing inherent risk would go up (international derivatives would likely be considered inherently risky), and control risk and detection risk would be unchanged.
3) Inherent risk up, detection risk unchanged.
AUD 99
BEC 96
FAR 94
REG 96
.