Book 4 - Topic 41 - Page 97 - Paragraph 2
In the Black’s approximation, it says:
“Since Black’s approximation values the American option as the great of of the two values ($6.26 > $6.05), we would value this option at $6.26.”
Isn’t $6.26 the value of the European option as per the example on page 95?
Insight on this is appreciated, thanks
We are comparing two values here because we can either early exercise the option before the second dividend payment with the value of $6.05 or wait until the end of contract period with the value $6.26 (like European option: can only be exercsised at the end of period).
The explanation seems correct. Since it is a know thing that the value of the American option can NEVER be less than a european option of the same tenor and underlying, so it has to be atleast valued at par with the Euro option. However now, the holder has an option to early exercise, hence the choice given, but at $6.05 it would have violated the first principal and could become a source of arbitrage trading. Hence it is correct to state the value is $6.26 (Carefult, because of early exercise it is not VALUED more than $6.26 i.e. the european option
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Thanks for the feedback guys.