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Subtracting a writer’s received premium

A writer’s premium is an initiation receipt, so simple profit adds it to the negative holder settlement.

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Recognize the double-outflow record

For a fictional short put, premium 5 is received and holder payout at expiry is 10. A calculation −10−5=−15 treats the received premium as if the writer paid it.

Restore the receipt sign

Correct simple writer profit is −10+5=−5. The matching holder pays 5 and receives 10, earning +5. These sides sum to zero in the stipulated no-cost model.

Original sign repair
SidePremiumSettlementSimple profit
Holder−5+10+5
Writer+5−10−5

Do not change the quoted premium itself

A premium quote can be positive 5 for both sides. The position determines its signed cash flow. Changing the quote to a negative premium can hide which field represents a price and which represents a payment.

Keep other obligations separate

A premium receipt does not eliminate margin, settlement or risk. The repair is an accounting correction for the model, not a claim that the writer has no further funding need.

Further references