# What is the strike of a short put that mimics a covered call

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?

## 1 Answer

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!