Option Strategies: Payoffs, Construction and Risk

How option legs combine into spreads, straddles, condors, calendars and covered positions: exact construction, expiry payoffs, portfolio Greeks and execution risk.

An option is a contract. A strategy is what you do with several of them. This chapter is about the second part: how legs combine, what the combination pays at expiry, which exposures it carries, and what can go wrong between deciding on it and settling it.

It assumes the instrument itself: premium, intrinsic and time value, the Greeks and the volatility surface. Those are covered in the Options chapter and are not repeated here. For where option strategies sit among all trading approaches, see Trading Strategies.

Read this before any payoff diagram

An expiry payoff diagram shows one instant: the moment the contract expires. It is the value of the basket if every leg runs to expiry and settles. It is not the value of the position today, tomorrow or at any other time before expiry.

Before expiry, the same basket is worth something between its intrinsic value and its expiry payoff, and the difference depends on implied volatility, time remaining, interest rates and, for a stock, the expected dividend. A long straddle that the diagram shows making money at a 10% move may be worth less than it cost for months, even while the underlying is moving. A credit spread that the diagram shows losing only at the far edge can lose sooner than the diagram suggests if volatility rises and the whole curve shifts.

Two consequences worth carrying through the chapter:

• Every diagram here is labelled at expiry. Treat it as the settlement arithmetic, not as a forecast.
• A calendar or diagonal spread has no single expiry curve at all. Its legs expire on different dates, so by the time the far leg is being settled the near leg has already gone. There is no one date at which the whole basket pays off together.

Every number in this chapter is calculated by one piece of code (src/lib/optionPayoff.ts), which the diagrams, the tables and the worked examples all read from, and which the test suite checks against closed-form results. The premiums are hypothetical, chosen to make the arithmetic legible. They are not quotations, and nothing here is a lot size, an expiry date or a margin rate.

How the arithmetic works

For a European-style option held to expiry, each leg is worth its intrinsic value and nothing more:

• A call is worth max(underlying − strike, 0).
• A put is worth max(strike − underlying, 0).

The position’s result per unit is the sum over legs of the signed quantity times the leg’s intrinsic value, less what the legs cost:

result at expiry = Σ  quantity × ( intrinsic(leg) − premium(leg) )

A leg bought is a positive quantity; a leg sold is negative. The net premium is Σ quantity × premium: positive when the basket cost money to open (a net debit), negative when it took money in (a net credit). This is the sign convention throughout, and it is why a long option’s chart sits below the axis at a price where it expires worthless.

Two units of a leg are written as a quantity of 2, or −2 when sold.

Directional spreads

A vertical spread buys one option and sells another of the same kind and the same expiry at a different strike. Selling the leg you do not need pays for part of the leg you do, which lowers the cost and caps the payoff.

Bull call spread

A view that the underlying will rise, with the upside deliberately capped.

Net debit ₹5 per unit. If the basket is sized at 500 units, that is ₹2,500 paid to open it. The 500 is a stated quantity for the illustration, not a contract size.

At expiry, with the underlying at S:

• Below 100: both calls expire worthless, and the position loses the ₹5 it cost.
• Between 100 and 110: the long call has value, the short call does not.
• Above 110: both are in the money and the spread is worth the 10-point strike distance.

Maximum profit is therefore 110 − 100 − 5 = ₹5, maximum loss is ₹5, and the break-even is 100 + 5 = ₹105. The diagram above computes all three.

The trade is explicit: the ₹3 received for the 110 call paid for part of the 100 call, and bought a ₹5 reduction in cost in exchange for giving up everything above 110.

Bear put spread

The mirror image for a fall, again with the payoff capped.

Net debit ₹5. Maximum profit 110 − 100 − 5 = ₹5 when the underlying finishes at or below 100, maximum loss ₹5 above 110, break-even 110 − 5 = ₹105.

Bull put spread

A credit spread: money is received now, and the risk is the strike distance less that credit.

Net credit ₹4. Maximum profit ₹4 if the underlying finishes at or above 100. Maximum loss is (100 − 90) − 4 = ₹6, at or below 90. Break-even 100 − 4 = ₹96.

The long 90 put is what bounds the loss. Without it this is a naked short put, whose loss runs to the underlying reaching zero, and which the engine would report as a bounded but very large number rather than as ₹6.

Bear call spread

Net credit ₹4. Maximum profit ₹4 at or below 100. Maximum loss (110 − 100) − 4 = ₹6 at or above 110. Break-even 100 + 4 = ₹104.

What “defined risk” means, and what it does not

For all four spreads, the contractual payoff at expiry is bounded, and the bound is arithmetic: strike distance against net premium. That is a statement about the settlement calculation, and only about that.

It does not mean the position cannot lose more than the diagram’s worst case in practice. It means the contractual expiry payoff is bounded. What sits outside that bound is everything operational: a protective leg that came back rejected or only partly filled, a position closed early at a worse price, a market where the far strike is untradeable, an assignment you did not expect. Section 12 deals with those.

Large-movement and volatility structures

A long straddle buys movement without taking a direction. It profits only if the move is large enough to cover both premiums: at a 100 strike costing ₹11, the underlying must finish below 89 or above 111. That the underlying moves is not sufficient; it must move enough.

A short straddle is the other side of the same trade. It collects ₹11, keeps it if the underlying finishes at exactly 100, and its chart falls away without limit in both directions. At a spot of 50 the diagram shows −₹39; the loss keeps growing below that.

A high proportion of profitable expiries is not the same as a good return. A short straddle can be closed profitably most months and still lose more in one month than it made in all of them. Selling volatility is not the same as earning a fixed income, and the chart is the reason.

The long strangle is the same bet as the straddle placed further out. Buying the 110 call and the 90 put costs ₹6 instead of ₹11, which lowers the break-even hurdle to 84 and 116, but leaves the region between them worthless at expiry.

Range and targeted-price structures

An iron condor sells the middle and buys the outside. It has four legs: two credit spreads, one either side of the current price.

Net credit ₹2. If the underlying finishes between 95 and 105, all four legs expire worthless and the ₹2 is kept. The short put is protected by the long 90 put, and the short call by the long 110 call, so the loss stops at the strikes: (95 − 90) − 2 = ₹3 on the downside and the same on the upside. Break-evens are 95 − 2 = ₹93 and 105 + 2 = ₹107.

The wings are what make this different from a short strangle. Without them the same premium would be collected and the chart would keep falling at both ends. With them, the risk is bounded, and the price of that bound is the premium given up for the wings.

Iron butterfly

An iron butterfly is the same construction with the two short legs at the same strike, and the wings placed equidistant around it.

Net credit ₹9. Maximum profit ₹9 if the underlying finishes exactly at 100, maximum loss (100 − 80) − 9 = ₹11 at or beyond either wing, break-evens at 100 − 9 = ₹91 and 100 + 9 = ₹109.

It concentrates the payoff on one price. Compared with the condor it collects more and is wrong over a much narrower range.

Long call butterfly

Butterflies can also be bought, which reverses the shape.

Net debit ₹2. Maximum profit 10 − 2 = ₹8 at exactly 100, maximum loss ₹2 outside the wings, break-evens 90 + 2 = ₹92 and 110 − 2 = ₹108.

Long condor

Net debit ₹2. Maximum profit ₹3 anywhere between 95 and 105, maximum loss ₹2 outside the 90 to 110 range, break-evens at ₹92 and ₹108. It is a butterfly with a flat top instead of a peak.

Time and volatility term structure

A calendar spread takes the same strike at two different expiries. A diagonal spread takes different strikes at different expiries.

There is no expiry payoff diagram for either, and no universal maximum profit, maximum loss or break-even formula. That is not a gap in this chapter. It is the structure. At the near expiry the short leg settles and disappears, while the long leg is still an option with time left, and what it is worth then depends on where the underlying is, what implied volatility is, and how much time remains. No single curve describes both moments.

What a trader is actually evaluating is the relationship between two expiries:

• The volatility term structure, whether the near expiry is priced rich or cheap against the far one.
• How quickly the near leg’s time value decays relative to the far leg’s.
• What the far leg will be worth if the short leg expires worthless, which is not a fixed number.
• Where the underlying has to be, and when, for the position to be worth more than it cost.

Calling these “theta strategies” describes one input and ignores the others. A calendar spread is long one maturity’s volatility and short another’s, and its value moves when either reprices. A diagonal adds a directional exposure on top.

If a model-based valuation chart is used for these structures, it is a model output, not a payoff, and it must state every assumption behind it: the pricing model, the implied volatilities for both expiries, the interest rate, any dividend assumption, and the date being valued. A chart without those is not evidence of anything.

Covered and protective positions

These combine a position in the underlying with an option. The underlying is a linear leg here, worth its price at expiry, so it enters the same arithmetic as everything else.

Covered call. Own at 100, sell the 110 call for ₹3. The premium lowers the effective cost, and every rupee of it is kept if the underlying stays below 110. Above 110 the shares are called away at 110, so the gain stops at ₹13 per unit however far the underlying runs. On the downside the call premium softens the fall by ₹3 and nothing more: the shares can still fall a long way, and the loss runs to ₹97 if the underlying reaches zero. A covered call is not a low-risk position; it is a long position with the upside sold.

Protective put. Own at 100, buy the 95 put for ₹4. Below 95 the put pays, so the loss stops at (100 − 95) + 4 = ₹9 per unit. The cost is the ₹4 premium, which raises the break-even to ₹104, and the upside is untouched. This is insurance, and it is paid for like insurance.

Collar. Own at 100, buy the 95 put for ₹4 and sell the 110 call for ₹3, so the options net to ₹1. The outcome is bounded at both ends: maximum profit 110 − 100 − 1 = ₹9, maximum loss (100 − 95) + 1 = ₹6, break-even ₹101. The call paid for most of the put, and the price of that is the capped upside.

Advanced constructions

These need the same arithmetic plus an understanding of financing, execution and, in some cases, continuous rebalancing.

Ratio spread. Buy one 100 call at ₹8, sell two 110 calls at ₹3 each. Net debit ₹2. The payoff peaks at ₹8 at the 110 strike and then falls away, because one of the two short calls has no long call against it. The terminal slope is −1, so loss is unbounded above. A ratio spread is a position that contains a naked short option even though it has several legs.

Backspread. The reverse: sell one 100 call at ₹8, buy two 110 calls at ₹3 each. Net credit ₹2, worst case −10 + 2 = −₹8 at the 110 strike, unbounded profit above. It is a bet on a large move financed by the premium received.

Synthetic forward. Buy the 100 call at ₹7 and sell the 100 put at ₹5 for a net debit of ₹2. At any price the result is underlying − 100 − 2, a straight line, break-even ₹102. A synthetic long forward carries the economics of the underlying without holding it, which is the point and also the risk: no defined loss.

Box spread. A bull call spread combined with a bear put spread at the same two strikes produces a payoff that is constant at every price: the strike width. Buy the 100 call at ₹8, sell the 110 call at ₹3.20, buy the 110 put at ₹8.80, sell the 100 put at ₹3.90. Net debit ₹9.70, and the position is worth ₹10 at every expiry price, so the result is ₹0.30 regardless of where the underlying finishes. Whether that ₹0.30 is worth having depends on financing, margin, execution and what it costs to hold, which is where these trades are actually won or lost. A box priced above its width is a loss at every price.

Conversions and reversals. Combining an option position with the underlying to lock a relative price. They are sensitive to borrow costs, dividends, financing and the ability to trade the underlying at the assumed price, and they fail on those terms rather than on the payoff.

Delta-neutral positions and gamma scalping. A position can be arranged so its delta is near zero at a chosen price. It is not then without risk, because delta changes as the underlying moves. If gamma is positive, delta grows in the profitable direction as the underlying moves and the position has to be rebalanced to stay neutral; each rebalance realises a little of the movement, which is what gamma scalping means. That only works if the realised movement exceeds what was paid for the position, and it stops working in quiet markets. A nominally delta-neutral portfolio becomes directionally exposed the moment the underlying moves, and someone has to decide whether to keep rebalancing.

Volatility-surface relative value. Rather than betting on one option’s implied volatility rising or falling, these trades take opposing positions in the implied volatilities of different strikes, expiries or underlyings, and profit when the relationship between them returns to a level the trader considers normal. The exposure is to the relationship, and the risks are the relationship breaking rather than converging, plus whatever directional and volatility exposure is left over.

Portfolio Greeks

The Greeks of a basket are the sum of its legs’ Greeks, each multiplied by its signed quantity. That is the whole method. The Options chapter defines them; this section is about combining them.

Units matter, so they are stated:

• delta: units of the underlying per unit of the position, before any multiplier.
• gamma: change in delta per ₹1 move in the underlying.
• theta: result per calendar day, at the convention used here.
• vega: result per 1 percentage point change in implied volatility.

Take the bull call spread from the start of the chapter, with the underlying at 100, and suppose the two legs carry these per-unit values:

Multiplying each row by its quantity and adding:

For a basket of 500 units, each figure scales by 500:

• Delta 100 units of the underlying. A ₹1 rise moves the position by about ₹100, before gamma.
• Gamma 5. That delta is only valid at 100. After a ₹1 rise it becomes about 105 units, and after a ₹1 fall about 95.
• Theta −₹10 per day. Holding the position and nothing else happening costs about ₹10 a day.
• Vega +₹15 per point. A rise of 2 percentage points in implied volatility adds about ₹30, all else equal.

The Greek values in the first table are illustrative figures chosen to make the arithmetic checkable, not model output. The point is the method: sign the legs, add, scale. Note what the net table shows. The spread is long delta and long vega, and it costs theta, so it needs the underlying to rise or volatility to rise to make up for the time it spends open. That is a different description of the same position from the payoff diagram, and the two must agree.

These exposures do not stay put. As the underlying moves towards 110, the short call’s delta approaches 1 and the position’s net delta falls towards zero; gamma concentrates around the strikes as expiry approaches; theta grows in magnitude and then collapses at expiry; vega falls away for both legs. A position that was delta 100 units this morning is not that this afternoon.

Comparison matrix

Where a Greek is named, read it as the exposure at the assumed price, not as a label that travels with the strategy. Delta signs change as the underlying moves, and a ratio spread can move from long to short delta within a day.

What can go wrong between the decision and the settlement

This is where multi-leg positions actually fail, and none of it appears in a payoff diagram.

The basket is not executed atomically. Submitting four legs as one instruction does not mean four fills at one instant or at one price. Each leg is a separate order matched against a separate book. A spread is routinely half-filled, and a trader who owns the long call but not the short call is in a different and larger-risk position than the one they thought they had.

The protective leg is the one most likely to be missed. In a credit spread the protective wing is the cheap leg and often the less liquid one. If it does not fill, the position is not a spread. It is a naked short option with the payoff diagram of a naked short option, and it should be treated that way until the leg is on.

Liquidity and the spread. Option markets are less liquid than the underlying, strike by strike. Buying at the offer and selling at the bid is a real cost that a payoff diagram does not show, and it is usually worst exactly when a trader most wants to adjust, in a fast market. A leg that is untradeable at any sensible price turns a defined-risk structure into a position that can be entered but not left.

Margin is not static, and hedged margin treatment depends on the legs actually being there. Portfolio margin systems recognise a spread and charge against its bounded loss. When one leg closes, lapses, or is exercised early, that treatment can change, and the requirement can rise sharply with no change in the underlying price. A broker may also act on its own risk management: raise requirements, restrict new positions, or square off a position it considers under-margined, at a price the trader did not choose.

Expiry is a deadline with consequences, and the consequences differ by instrument. For contracts on individual securities the position does not vanish at expiry. Under NSE Clearing’s settlement mechanism, exercise is European style and final exercise is automatic on expiry: long positions at in-the-money strikes are assigned to short positions in the same series on a random basis, and settlement creates delivery obligations. An in-the-money short call means delivering the shares; an in-the-money short put means taking them and paying for them. A long option that finished in the money does not disappear either: it becomes a delivery, with the cash or shares that implies.

Index options settle in cash. Their final settlement price is based on the closing level of the underlying index on the last trading day, so an in-the-money index option settles by a credit or a debit and no shares change hands.

The practical difference is large. An index iron condor that finishes with one wing in the money is a cash settlement. A stock iron condor that finishes with one wing in the money can be a delivery obligation on shares, and the quantity is set by the contract, not by the trader’s account size. Whether a “Do Not Exercise” facility is available for a particular close-to-money stock option is a matter for the current exchange circular and the broker’s process, and it should be checked rather than assumed.

Mixed expiries carry mixed dates. A calendar spread has two settlement dates. The near leg settles while the far leg is still open, so the position the trader is holding after that date is not the position the diagram described, and its risk profile can be entirely different.

Early exit is not the same trade reversed. Closing a multi-leg position means paying the spread again on every leg. A structure opened for a ₹2 credit can cost more than ₹2 to close, and the adjustment trade a trader has in mind may not be available at the moment it is needed.

Exercise before expiry. Physical settlement and automatic exercise are the expiry mechanics; early exercise and early assignment in the contracts that permit it can arrive on a date the trader did not choose, usually around a dividend or when a short option is deep in the money.

The distinction worth keeping

An option strategy is a set of contractual payoffs plus an execution plan. The payoff is arithmetic and can be calculated exactly at expiry, which is what this chapter has done. The execution plan is where the losses that are not in the diagram come from.

A trader who can draw the payoff but has not thought about which legs might not fill, what the margin does if one closes, and what happens if an in-the-money short stock option becomes a delivery obligation has only done half of the work.

Further reading

• Options for premiums, the Greeks and the volatility surface
• Trading Strategies for where option strategies sit among all approaches
• Derivatives and Futures
• What it costs for brokerage, taxes and statutory charges
• Accounts, orders and product types for order mechanics
• Beware of option selling and Naked option buying works

Educational use only

This chapter is for education. It is not investment advice or a recommendation to implement any strategy described here.

Trading options carries financial risk. Writing options can involve losses larger than the premium received, margin obligations that change without notice, and, for contracts on individual securities, the obligation to deliver or pay for shares at settlement.

Every premium, strike and quantity here is hypothetical and chosen to make the arithmetic readable. They are not quotations, and they are not lot sizes, expiry dates or margin rates. Actual results depend on contract terms, prices, volatility, liquidity, execution, transaction costs and the applicable exchange and clearing rules, which change and which should be checked against the current NSE, NSE Clearing and broker documentation before any position is taken.