Question says Tony believes the price of an underlying, currently selling at $96, will increase substantially in the next 6 months, so he purchases a European call option expring in 6 months. The call has an exercise price of $101 and sells for $6. How much is the value of the potential credit risk? 1. Since potential credit risk is payments due in the future, why is potential credit risk not = 101-96=5? Is it because it is a European call option? The answer says potential credit risk is current market value of $6. 2. If the call option was an American style, would potential credit risk be 5?

Potential credit risk is just the value of the option. Before expiration American options can have current credit risk if the holder decides to exercise the option forcing the seller to deliver shares.

So potential credit risk for a European style option is its market value ($6), is that correct? Why is it not the payments due in the future which in the above example = $5

Yes. If you jumped forward to the expiration date, keeping everything the same, the option would be worth $5, but you have no idea what it will be worth in the future as the underlying stock price will change every day. The stock is currently trading below the strike price so the value that the option does have is entirely time value.

The payment in the future is not certain to be $5. However, the market value today is $6, so you have to use this number