If I am long a stock $X$ which I purchased at $\$100$ and sold a covered call in the front month with strike $\$105$ for $\$2$ then is it true that the covered call is equivalent to a naked put at strike $\$100 - \$2 = \$98$?

Am I missing something here?


This is not quite right.

The covered call you are describing is equal to selling a Put with the same strike price (\$105) and holding ( \$105 / (1+r) ) in the bank. If you draw the Payoff diagram this will become apparent.

Put call relationships are summarized as the Put-Call parity:

$$ S - C = D \cdot K - P $$ Where $S$ the underlying, $D$ is the discount factor and $K$ the strike price.

The left side is the covered call you are describing and the right side the Put plus cash. As a bonus, using this relationship you can calculate the no arbitrage price of the put!


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