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Option Payoff at Expiration

An option buyer pays a premium for a right; the writer collects it and takes on an obligation. Pick a position, set the strike and the premium, and see what it earns or loses at every stock price on expiration day, with the breakeven, the most you can make and the most you can lose. Then split today’s premium into intrinsic value and time value.

Series 65 Lesson 6.4 · also Lessons 5.3 and 8.3 · about 20 minutes

Across: the stock price on expiration day. Up: the position’s profit or loss. Click or drag on the chart to read any price; with the chart focused, the left and right arrow keys move $1 (Page Up and Page Down move $5).

Breakeven at expiration
Maximum gain
Maximum loss
Premium paid
Result at the chosen price
Shares controlled

Today’s premium: intrinsic value and time value

Stock price now
The option is
Intrinsic value
Time value

Profit and loss at key prices

Stock at expirationOption worthPer shareWhole positionNote

The same thing in a spreadsheet

The position

The contract

$
$
$

The stock

$
$

Try an example

From Series 65 Lesson 6.4; prices the lesson leaves open are made up for the example.

Rights and obligations

A call gives its buyer the right to buy 100 shares at the strike price until expiration; a put gives the right to sell at the strike. The buyer pays the premium and can walk away, so the most a buyer can lose is the premium. The writer (seller) keeps the premium and must deliver (call) or buy (put) if the option is exercised, so the most a writer can gain is the premium.

At expiration

call worth = max(0, stock − strike)

put worth = max(0, strike − stock)

Subtract the premium for a buyer, or add it for a writer, and you have the profit. That gives the breakevens:

call: strike + premium    put: strike − premium

The four corners and two combinations

  • Long call: gain unlimited, loss = premium.
  • Short (naked) call: gain = premium, loss unlimited: the stock has no ceiling.
  • Long put: gain = strike − premium (the stock can only fall to zero), loss = premium.
  • Short put: gain = premium, loss = strike − premium.
  • Covered call (own the shares, write a call): breakeven = cost − premium; gain capped at strike − cost + premium; loss = cost − premium if the stock goes to zero. Income for a holder willing to sell at the strike.
  • Protective put (own the shares, buy a put): breakeven = cost + premium; gain unlimited; loss limited to cost − strike + premium. Insurance.

Intrinsic value and time value

Before expiration, the premium has two parts:

premium = intrinsic value + time value

Intrinsic value is what exercising right now would be worth: stock minus strike for a call, strike minus stock for a put, never below zero. An option with intrinsic value is in the money; at the strike it is at the money; otherwise it is out of the money. Whatever is left of the premium is time value, the price of the chance that the stock moves before expiration. It melts to zero on expiration day.

In the money is not the same as profitable. A buyer who paid $3.50 for a 45 call is in the money at $47 but still needs $48.50 to break even.

Check yourself

  1. A 40 call trades at $5.25 with the stock at $43. Find the intrinsic value, time value and breakeven.
    Answer

    Intrinsic $43 − $40 = $3.00; time value $5.25 − $3.00 = $2.25; breakeven $40 + $5.25 = $45.25.

  2. An investor buys an ABC 60 put for $4. Find the maximum loss, maximum gain and breakeven for one contract.
    Answer

    Loss: the $400 premium. Gain: ($60 − $4) × 100 = $5,600 if ABC goes to zero (not unlimited). Breakeven $56.

  3. An investor writes a 35 put for $2. What are his maximum gain and loss per contract?
    Answer

    Gain: the $200 premium. Loss: ($35 − $2) × 100 = $3,300, if he must buy at $35 a stock that has fallen to zero.

  4. She bought 100 shares at $62 and a 60 put for $1.50. What is her worst case, and her result if the stock rises to $75?
    Answer

    Worst case: sell at $60 through the put, losing $2 on the shares plus the $1.50 premium: $350, however far the stock falls. At $75: $13 − $1.50 = $11.50 a share, $1,150.

A bit of history: Aristotle tells how Thales of Miletus paid small deposits in winter for the use of every olive press at harvest, and profited when a great crop came: the right without the duty, the oldest option on record.

“A prudent man foreseeth the evil, and hideth himself; but the simple pass on, and are punished.” — Proverbs 22:3