Hello David,
While doing Hull ex. 09 18, I encountered an issue:
In your solution (cf http://www.bionicturtle.com/wiki/Hull.09.18/), you state:
"P>=c + K*EXP[-rT] - S0
and since c = C,
P >= C + K*EXP[-rT] - S0, or
C - P >= S0 - K*EXP[-rT]"
I don't understand why c=C. For me, C>=c due to the fact that American options have more "optionality", hence, more value and thus, C>=c (cf. Hull Chapt 9, p212). The only thing that makes me think that C could equal c is the fact that an American call options with no dividend should never be exercised early. In this specific case (=no dividend), an American option is thus equal to an European option. Am I right, or is it something flawed in my "reasoning" ?
Also, please notice that the sign of the last equality is in the wrong direction : it should be C - P <= S0 - K*EXP(-rT).
You also use c=C in the second part of the proof, but here, given the direction of the inequality c + K >= P + S0 => C + K >= P + So, so it is not a problem (both C=c or C>=c keeps the inequality true).
Thanks in advance !
Best regards,
trabala38
While doing Hull ex. 09 18, I encountered an issue:
In your solution (cf http://www.bionicturtle.com/wiki/Hull.09.18/), you state:
"P>=c + K*EXP[-rT] - S0
and since c = C,
P >= C + K*EXP[-rT] - S0, or
C - P >= S0 - K*EXP[-rT]"
I don't understand why c=C. For me, C>=c due to the fact that American options have more "optionality", hence, more value and thus, C>=c (cf. Hull Chapt 9, p212). The only thing that makes me think that C could equal c is the fact that an American call options with no dividend should never be exercised early. In this specific case (=no dividend), an American option is thus equal to an European option. Am I right, or is it something flawed in my "reasoning" ?
Also, please notice that the sign of the last equality is in the wrong direction : it should be C - P <= S0 - K*EXP(-rT).
You also use c=C in the second part of the proof, but here, given the direction of the inequality c + K >= P + S0 => C + K >= P + So, so it is not a problem (both C=c or C>=c keeps the inequality true).
Thanks in advance !
Best regards,
trabala38