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Calculate a protective put’s terminal floor and cost

Stock purchased at 100 plus a 90 put costing 3 has terminal value max(S,90) and simple profit max(S,90)−103.

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Specify both original legs

The position holds one stock unit purchased at 100 and one same-unit put with strike 90 and premium 3. No underlying income, financing or other cost is supplied.

Add the put payoff to the stock

Terminal value is S+max(90−S,0)=max(S,90). Below 90, the put fills the difference up to 90. Above 90, the put expires with zero payoff while the stock contributes S.

Retain the premium in the cost

Initial unfinanced cost is 100+3=103. Thus the simple profit floor is 90−103=−13, not −10. At S=103 the simple position profit is zero.

Original protective-put scenarios
Terminal priceCombined terminal valueSimple profit
090-13
8090-13
9090-13
100100-3
1031030
12012017

Name what is protected

The model creates a terminal-value floor under the matching-unit assumed settlement. It does not make every interim marked value constant or remove the option’s cost. Contract exercise and settlement rules require their own record.

Further references