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Reconcile a short put’s premium and settlement

A short put with strike 100, received premium 5 and terminal price 90 has simple profit −5 per unit.

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Record the initial receipt

The writer receives 5 at initiation for the fictional put. A received premium is positive cash for this side. The holder pays the same amount under the no-cost contract comparison.

Apply the negative holder payoff

At terminal price 90, the put holder payoff is max(100−90,0)=10. Writer settlement is −10. Adding the premium receipt gives simple profit −10+5=−5.

Inspect other terminal prices

Original short-put scenarios
Terminal priceWriter settlementSimple profit
0-100-95
90-10-5
95-50
10005
12005

Use the supplied nonnegative-price domain

Under this one-unit simple model, minimum profit occurs at S=0 and is −95; maximum is the received 5 when the holder payoff is zero. Margin, assignment and settlement funding are separate questions not modeled by these bounds.

Further references