Common mistake 1 with Option strategies (payoff & profit)

Reading maximum profit without the probability of reaching it. Wide-winged strategies show large maxima that are rarely hit.

Common mistake 2 with Option strategies (payoff & profit)

Forgetting the premium when computing breakeven.

Common mistake 3 with Option strategies (payoff & profit)

Selling uncovered calls without noticing the loss is unlimited.

Common mistake 4 with Option strategies (payoff & profit)

Ignoring early assignment risk on short American options near ex-dividend dates.

EconStatsCraft › Option strategies (payoff & profit)

Option strategies (payoff & profit)

Draws the payoff of a multi-leg option position at expiry, prices each leg with Black–Scholes, and reports the net cost, breakevens, maximum profit and loss and the probability of finishing in profit.

The intuition

A single option gives a hockey-stick payoff. Adding options with different strikes, or the stock itself, bends that line into almost any shape: capped, floored, V-shaped or tent-shaped. Each strategy is a view on where the stock will be, or how much it will move, paid for with the premium.

When to use it

Expressing a view on direction or volatility, insuring a holding, generating income from a stock you own, or answering a CFA or FRM question on breakevens and maximum profit or loss.

Where the estimator comes from

Each leg's payoff at expiry is linear on either side of its strike: a call pays \max(S_T-K,0), a put \max(K-S_T,0) and the stock S_T. A strategy's payoff is the weighted sum, so it is piecewise linear with kinks at the strikes. Profit subtracts the net premium carried to expiry, (\sum_i q_i c_i)e^{rT}. Breakevens are the roots of the profit line, and put-call parity, C-P=S-Ke^{-rT}, shows why some strategies are equivalent.

The model

\text{Profit}(S_T) = \sum_{\text{legs}} q_i\,\text{payoff}_i(S_T) \;-\; \text{net premium}\times e^{rT},\qquad \text{call payoff} = \max(S_T-K,0)

What it assumes

European options held to expiry; early exercise and early closing are ignored.
Premiums come from Black–Scholes at one volatility. Real quotes include a skew, so out-of-the-money puts usually cost more than shown.
The probability of profit uses a lognormal stock price drifting at the risk-free rate. It is a guide, not a forecast.
No transaction costs, margin or taxes.

Statistical properties

Spreads trade upside for a lower cost: the short leg finances part of the long one.
Straddles and strangles profit from large moves in either direction and lose from time decay if the stock stays still.
A butterfly profits most if the stock ends exactly at the middle strike.
Covered call and short put, and protective put and long call, have the same profile by put-call parity.

How to read the output

A bull call spread pays for part of the long call by selling a higher strike: cheaper, but capped.
A long straddle profits only if the move exceeds the total premium in either direction. That is a bet on volatility, not direction.
A covered call and a short put have the same payoff shape; a protective put and a long call do too. That is put-call parity.
The dashed line shows the position halfway to expiry. Time value smooths the kinks, which is why positions rarely trade at their expiry payoff.

A worked reading

A bull call spread: buy the 95 call for 10.79 and sell the 105 call for 5.78, with the stock at 100, six months to expiry, 25% volatility and a 4% rate. Net cost is 5.01. At expiry the spread pays at most 10, so the maximum profit is 4.89 after carrying the cost forward, the maximum loss is the 5.11 paid, and it breaks even at a stock price of 100.11. On these assumptions it finishes in profit about half the time, 50.8%.

Symptom → diagnosis → what to do

If you see this	It means	Do this
Maximum profit shows as unlimited	An uncapped long call or stock leg	Correct for long calls, straddles and protective puts
Breakeven missing	The position is profitable or loss-making at every price	Check the strikes and the premium
Probability of profit looks low	Strategy needs a large move	Typical for straddles and wide spreads
Strikes ignored	Strategy uses fewer strikes than entered	Each strategy names the strikes it uses

Common mistakes

Reading maximum profit without the probability of reaching it. Wide-winged strategies show large maxima that are rarely hit.
Forgetting the premium when computing breakeven.
Selling uncovered calls without noticing the loss is unlimited.
Ignoring early assignment risk on short American options near ex-dividend dates.

Where to read this properly

Hull, Options, Futures and Other Derivatives (2021), ch. 12, Trading Strategies Involving Options.
CFA Institute, Derivatives: Option Strategies (Level III).

Related Finance & risk

Black–Scholes option pricing · Bond price, duration & convexity · Merton distance to default · EMI / home loan planner · CAPM / beta estimation · Multi-factor model · Portfolio optimization · Value at Risk & Expected Shortfall · Performance & drawdown · Time value of money & NPV/IRR · Equity valuation (DDM, FCF, residual income) · Cost of capital (WACC) · Binomial option pricing · Forwards, futures & swaps · Credit risk & Basel capital · Extreme value theory (tail risk)

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Each example is simulated from a known model, so you can check whether the estimator recovers the truth - and nothing here is anyone's private data.

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Option strategies (payoff & profit)

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

See also

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