FINC6010 Chap.6 Options Positions, Payoffs and Profit
Options Positions, Payoffs and Profit
Option mechanics begin with rights and obligations. This chapter distinguishes calls from puts, long positions from writers, and European from American exercise. It builds terminal payoffs with max functions, then shifts payoff into profit by including premium. Labelled graphs show strike, break-even, slope and loss bounds so words, formulas and geometry remain consistent.
A call holder may buy at the strike, while a put holder may sell. Writers receive premium and accept the corresponding contingent obligation. European and American labels concern exercise timing, not trading venue. Terminal payoff ignores the initial premium; profit incorporates it and therefore crosses zero at a different price from the strike.
The holder’s max function creates a floor at zero payoff, while the writer’s payoff is its negative. Long-call loss is limited to premium, whereas short-call loss can keep expanding as the underlying rises. A long put benefits from declines below strike, while a short put accepts downside exposure in exchange for premium.
Each diagram must label terminal underlying price on the horizontal axis and payoff or profit on the vertical axis.
What this chapter covers
- 01
Call and put rights
- 02
Long and short positions
- 03
European and American exercise
- 04
Terminal max functions
- 05
Premium and break-even
- 06
Profit diagram slopes and bounds
Worked example · free
Separate call payoff from profit
- 1Evaluate max of terminal price minus strike and zero.
- 1Subtract premium for the holder’s profit.
- 1Reverse payoff and add premium for the writer.
- 2Check that paired profits sum to zero when financing is ignored.
Key terms
- Exercise price
- The contractual price at which the option holder may buy or sell the underlying.
- Intrinsic value
- The immediate exercise value, bounded below by zero for an option holder.
- Option premium
- The price transferred for the option right, subtracted from holder payoff and added to writer payoff when simplified profit is measured.
- Break-even price
- The terminal underlying price at which option profit is zero after incorporating premium under the assumptions stated in the problem.
- Option writer
- The short party that receives premium and must perform the contractual purchase or sale if the holder validly exercises.
- Profit diagram
- A graph of terminal option payoff adjusted for premium, with underlying price on the horizontal axis. Unlike a payoff diagram, its zero crossing marks break-even, while the strike remains the point where the exercise slope changes. Axis units must match the reported result.
Options Positions, Payoffs and Profit FAQ
What is the difference between a call and a put?
A call gives its holder the right to buy the underlying at the strike price. A put gives the holder the right to sell. The buyer chooses whether to exercise, while the writer receives premium and must perform if exercise occurs.
When is an option in the money?
A call is in the money when terminal underlying price exceeds strike; a put is in the money when terminal price is below strike. In-the-money status describes positive intrinsic value, not necessarily positive profit after the premium is included.
How do I find option break-even?
For a long call with premium measured at expiry on the simplified diagram, break-even is strike plus premium. For a long put it is strike minus premium. If financing or contract multipliers matter, incorporate them before reporting the final monetary result.
Can an exercised option still lose money?
Yes. Exercise depends on positive intrinsic value at expiry, while total profit also reflects premium. A call that finishes slightly above strike should be exercised, yet its payoff may remain smaller than the premium paid. Ignoring exercise would make the holder's loss larger, not restore the premium.
Exam move
Create a four-quadrant card for long call, short call, long put and short put. Record right or obligation, max payoff, premium sign, maximum gain, maximum loss and break-even. Check three graph points: zero, strike and a price above strike. Translate each position through four representations: a sentence, a max function, a terminal-value table and a labelled graph.
If any representation disagrees, return to the right or obligation rather than adjusting the picture by eye. Practise separating the exercise decision from total profitability: an option can be worth exercising while the trade still loses money after premium. Mirror every long result into its short counterpart and verify that paired payoffs sum to zero before transaction costs.
Change the premium without moving the strike kink, then change the strike without treating premium as intrinsic value. Finish by stating loss bounds and break-even in words, because those features are easier to audit than a memorised shape.
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