Option Basics - Calls, Puts, and Payoffs › Short Option Positions

Michael BrenndoerferNovember 15, 20253 min read
Quantitative FinanceAll chapters
Part 3 of 15Forwards, Futures, and Options
Chapter 18Option Basics - Calls, Puts, and Payoffs › Short Option Positions
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Selling (writing) options generates immediate income from the premium but creates potentially large obligations. Short option positions have mirror-image payoffs to long positions. While you pay premium for limited-risk exposure in long positions, you collect premium in short positions in exchange for assuming risk that can be substantial.

Out[9]:
Visualization
Line chart showing short call profit versus stock price with capped gains and unlimited losses.
Short call profit profile showing capped gains and unlimited risk. The seller collects the premium upfront but faces unlimited potential losses if the stock price rises significantly above the strike.
Line chart showing short put profit versus stock price with capped gains and large potential losses.
Short put profit profile showing capped gains and substantial downside risk. The seller keeps the premium if the stock remains above the strike but faces increasing losses as the stock price falls toward zero.

Short options have risk profiles that warrant careful attention:

  • Short calls profit when the stock stays below the strike. Maximum profit equals the premium received. However, if the stock rises significantly, losses grow without bound. Writing naked (uncovered) calls is one of the riskiest strategies in options trading. Because stock prices have no theoretical upper limit, the potential loss is unlimited.
  • Short puts profit when the stock stays above the strike. Maximum profit equals the premium. Losses are capped because the stock can only fall to zero, but this can still mean substantial losses (up to K−PK - P per share). A short put on a $100 strike with a $4 premium could lose up to $96 per share if the stock goes bankrupt.

As an option seller, you may hedge your exposure through delta hedging, which we'll explore in later chapters. If you write options, you should understand that the premium received is compensation for assuming potentially large risks.