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An Assignment is just opposite to an Exercise in Options. In Assignment, the buyer or seller of the Option exercises his right to buy or sell. When an Option is exercised, the stock exchange uses a trading software to randomly select a seller or buyer to honor the contract.
Suppose you have sold Tata Motors 350 call with premium received of Rs 15. The price of Tata Motors stocks moves up to Rs 380. In such a case, it is possible that some trader who has bought Tata Motors 350 call would choose to exercise his Option. And, if you are assigned by the software to honor the contract then you have to bear the loss of Rs 30 - Rs 15 = Rs 15 and honor the contract.
Only a small part of Options traded is assigned. All option holders have the right to exercise their options irrespective of the profitability or loss in the trade.
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