A single option gives a kinked payoff: zero below (for a call) or above (for a put) the strike, and linear beyond it. By combining options — and sometimes the underlying stock — a trader can manufacture almost any payoff profile. This is payoff engineering, and it matters for two reasons. First, it is how structured products are built: the principal-protected note is nothing but a zero-coupon bond plus an ATM call. Second, understanding these combinations deepens intuition about what option prices contain — a bull spread is a bet on direction with limited risk, a butterfly is a bet on realised volatility being low, a straddle is a pure volatility bet. Each position corresponds to a view, and the cost of entering it is the option market's price for that view.
Learning objectives. After this note you should be able to:
- set up a covered call and a protective put using put-call parity to understand each strategy's equivalence to a simpler option;
- construct a bull and bear spread from calls or puts and tabulate their payoffs;
- describe the box spread as a risk-free bond replicator and explain why it only works for European options;
- construct a butterfly spread and explain the market view it expresses;
- describe the calendar spread and its payoff profile;
- distinguish a straddle from a strangle in terms of cost, breakeven, and risk;
- articulate the payoff engineering theorem: any piecewise-linear payoff can be approximated by butterfly spikes.
In this lesson
- Single option plus underlying: covered call and protective put
- Spreads
- Combinations
- Payoff engineering: the butterfly as a building block
Before you start
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