Put Call Parity with American Call Option

[troubleshooter]

David: Regarding that one question where European Put Option price is given, also given are exercise price, time to maturity (6 months), risk free rate and current price of underlying. Next divident is in nine months. So it absolutely rules out possibility of a dividend during the terms of both options. The call of course is American option. As the underlying is guaranteed to pay no dividend for the term, I though you could use european put call formula for this. At least I think that's the way the question is meant to be looked at.

 

[David Harper CFA FRM]

Hi NewTurtle,

Thanks, I hadn't seen the complete question. Yes, I totally agree, without dividends, we can assume C=c (Amer = Euro) and put-call parity without inequality is preserved (i.e., it is the American put that introduces the inequality since P>= p)

... but at the same time, IMO that is advanced and arguably beyond the assigned scope. Your instincts here are fabulous but this depends on very specific information conveyed by Hull outside the assignment...an FRM candidate (again, just my opinion) would justifiably see the American call and rely on Hull's "put-call parity is only valid for European options" (Hull 9 convers all Euro and all American, this sort of variation is very tricky, it is NOT covered into Hull 9, and C>= c would be quite understandable given our assignments)....

David