Calls and puts

What each one pays at expiry, drawn as a payoff chart, from the buyer's side and the seller's.

6 minute read

A call is the right to buy. A put is the right to sell. This chapter looks at what each one is worth on its expiry date.

Expiry is the easiest moment to study. Time value has run out, so an option is worth its intrinsic value and nothing else. A $100 call with the stock at $112 is worth exactly $12 a share. With the stock at $95 it is worth nothing.

The payoff chart

Traders draw this as a payoff chart. Across the bottom is the stock price on the expiry date. Up the side is your profit or loss on one contract, after the premium you paid.

Take the call from chapter 1: a $100 strike that cost $3.02 a share, or $302 a contract. Below $100 the line is flat. The call is worthless and you have lost the $302. Above $100 the line climbs $100 for every $1 the stock gains, because a contract covers 100 shares.

You break even at $103.02. That is the strike plus the premium. Above it, you make money.

Stock price on the expiry date$110.00

Buying one $100 call for $302: profit or loss per contract at expiry

Drag across the chart, or focus it and use the arrow keys, to change the stock price on the expiry date.

Breakeven: $103.02
Most you can lose: $302
Most you can make: No limit

At $110.00 this call pays $10.00 a share, or $1,000 a contract. You paid $302 for it, so you are up $698.

One contract (100 shares) with a $100 strike. The premiums are the model prices from chapter 1: $3.02 for the call and $2.69 for the put. Green shading is profit, red is loss.

The other side of the trade

Every option has a buyer and a seller. The seller, also called the writer, collects the premium up front. In return the seller takes on the duty. If the buyer uses the option, the seller must deliver.

So the seller’s chart is the buyer’s chart turned upside down. Every dollar one side makes, the other side loses. Switch the diagram to Sell to see it.

Now compare the numbers under the chart. A call buyer can lose at most $302. A call seller’s loss has no limit, because a stock price has no ceiling. This is why brokers ask for extra approval and collateral before you can sell calls on shares you don’t own.

Puts

A put buyer profits when the stock falls. The $100 put cost $2.69, so it breaks even at $97.31: the strike minus the premium.

A put’s gain does have a ceiling. A stock can’t fall below zero, so the most a $100 put can pay is $100 a share. After the premium, that caps the profit at $9,731 a contract.

These charts show only the end point. Before expiry, an option still has time value. Its value curve is smooth instead of a sharp corner at the strike. How steeply that curve rises is the first Greek, delta.

Try it on real data

Start with a single SPY call or put and drag the stock price across its payoff. Then flip it from buying to selling.

Build a payoff on SPY