The text states: the party holding the long position can exercise the option. when thishappens, the party holding the short position is said to be assigned on the option. forthe owners of call options, the act of exercising involves buying the underlying assetfrom the assigned writer at a price equal to the strike price. for the owners of putoptions, exercising involves selling the underlying asset to the assigned put writer at aprice equal to the strike price.in this context, assigned means that the option writer is assigned the task of fulfillinghis or her obligation. for example, if you wrote a call and the call buyer exercised hisor her option to buy shares at the strike price, you might get a call from your brokertelling you that youve been assigned. you would have to sell shares to the call buyerat the exercise price, thus fulfilling your obligation as a call writer.