Payoff Diagrams and Moneyness
9 min read
Option positions are understood through pictures: payoff at expiry as a function of the underlying's final price. The diagrams are piecewise-linear, built from a small kit of parts, and fluency means translating between contract, picture, and formula without friction. Moneyness supplies the vocabulary for where the underlying currently stands relative to the kinks.
The building blocks
Every expiry diagram is assembled from four elementary shapes: the underlying itself (a diagonal line, slope +1 everywhere), cash (a horizontal line), calls (flat at zero left of the strike, then slope +1), and puts (slope up to the strike, then flat). Short positions flip each shape upside down. Adding positions adds their diagrams pointwise, so any piecewise-linear payoff with kinks at strikes can be manufactured, and read back, kink by kink: each kink of size in slope is an option at that strike.
The two option shapes, strike 100
The call is flat then rising; the put is falling then flat. Short positions are these shapes reflected through the zero line, and every strategy diagram is a pointwise sum of such parts.
A payoff is flat at below 90, rises with slope 1 from 90 to 110, and is flat at above 110. The slope changes: at 90, at 110.
A bull call spread (the strategies lesson names it). The levels pin the premium: flat at on the left means the structure cost 5 net. Slope changes locate the options; the resting level locates the cash.
The diagram, reconstructed
Slope +1 switches on at 90 (the long call) and off at 110 (the short call); the resting level of -5 is the net premium paid.
Moneyness
An option is in the money (ITM) when exercising now would pay: for calls, for puts. At the money (ATM): . Out of the money (OTM): exercise would pay nothing. Moneyness describes the option's current relationship to its strike, not its profitability.
Moneyness organises option behaviour so thoroughly that most of this course's statements are indexed by it. Deep ITM options move nearly one-for-one with the underlying (they are almost the asset); deep OTM options barely move (they are almost nothing); ATM options sit at the kink, maximally sensitive to which side the underlying ends on, and they carry the most optionality per unit of premium. The Greeks module makes each of these statements quantitative.
Breakeven levels
Premium c or p paid. The profit diagram is the payoff diagram shifted down by the premium; breakevens are where the shifted diagram crosses zero.
Underlying at 100. The 90 call is ITM by 10; the 110 call is OTM. The 90 put is OTM; the 110 put is ITM by 10. A move to 105:
Calls and puts partition the strike axis oppositely, which is why the same move improves one side's options as it erodes the other's, and why (next module) a call and put at the same strike are two views of one object.
Common trap
ITM does not mean profitable, and OTM does not mean worthless before expiry. An ITM option bought expensively can lose money (the premium exceeds the final payoff), and an OTM option retains value from the possibility of finishing ITM, the time value of the next lesson. Moneyness is a statement about NOW; profit is a statement about the whole trade.
Quick check
The underlying trades at 84. By how much is the 80-strike call in the money?
Quick check
A 120-strike put is bought for 7. What is the breakeven underlying price at expiry?
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