American Option has current credit risk and potential credit risk. Should’t the current credit risk be the value of the option? But the answer from Kaplan says the current credit risk is zero as the holder has no intention to exercise the option. So the potential credit risk should be the option’s value.
Does it make sense?
Current credit risk is zero because the option is out of the money, so there is no counter-party risk to begin with.
European options have no pay- ments due until expiration. Hence, they have no current credit risk until expiration, although significant potential credit risk exists.
Consider a European call option for which the underlying security has a price of 52.75 and a standard deviation of 0.35. The exercise price is 50, the risk-free rate is 4.88 percent continuously compounded, and the option expires in nine months. Using the Black–Scholes–Merton model, we find that the value of the option is 8.5580. The holder thus has potential credit risk represented by a present claim of 8.5580. This amount can be thought of as the amount that is at risk, even though at expiration the option will probably be worth a different amount. In fact, the option might even expire out of the money, in which case it would not matter if the short were bankrupt. If the short declares bankruptcy before expiration, the long has a claim on the value of the option under bankruptcy law.
If the option were American, the value could be greater. Moreover, with American options, current credit risk could arise if the option holder decides to exercise the option early. This alternative creates the possibility of the short defaulting before expiration.