Cash-and-carry arbitrage buys an asset and sells an overpriced forward or futures contract. The options equivalent is a conversion: long stock, long put and short call with the same strike and expiration. Reverse cash-and-carry shorts the asset and buys the relatively cheap forward; its options equivalent is a reverse conversion (reversal): long call, short put and short stock.
When strikes, expirations, contract terms and settlement all match, these combinations can lock a known terminal value. They are not automatically risk-free in a live account: financing, dividends, stock-borrow fees, bid-ask spreads, commissions, margin, assignment and settlement details can consume the theoretical parity gap or create operational risk.
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Cash-and-carry and reverse cash-and-carry at a glance
Cash-and-carry is a relative-value trade between an asset’s spot price and a forward or futures price. If the future is too expensive after allowing for interest, dividends, storage or other carrying costs, a trader can buy the asset, sell the future and carry the asset until delivery. The delivery proceeds repay the financing, leaving the mispricing as a locked spread if execution and settlement are reliable.
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Reverse cash-and-carry reverses those positions. The trader sells or shorts the expensive spot asset and buys the relatively cheap future. The short-sale proceeds are invested or used to meet financing needs while the future replaces the asset later. CISI describes this direction as selling the expensive cash asset and buying the cheap future.
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Listed options express the same financing relationships through put-call parity. A conversion combines long stock, a long put and a short call. A reversal combines short stock, a long call and a short put. In both cases, the option strike and expiration must match, and the options must reference the same underlying as the stock or future.
| Feature | Cash-and-carry / conversion | Reverse cash-and-carry / reversal |
|---|---|---|
| Underlying position | Long stock or other underlying | Short stock or other underlying |
| Option legs | Long put and short call | Long call and short put |
| Economic comparison | Own and carry the asset versus the synthetic forward or future | Short and finance the asset versus the synthetic forward or future |
| Primary friction | Funding cost, dividends, spreads, assignment and capital usage | Stock-borrow availability and fee, margin, dividends, spreads and assignment |
| Most important check | Carry-adjusted parity gap after all execution costs | Carry-adjusted parity gap with borrow available for the full holding period |
Put-call parity: the pricing relationship behind both trades
For a non-dividend-paying stock, the standard relationship is:
c = S + p − K e−r(T−t)
- c is the call value.
- S is the current stock price.
- p is the put value.
- K is the strike price.
- r is the continuously compounded risk-free interest rate.
- T − t is the time remaining to expiration.
The equation says that a call, a stock position and a put can be exchanged for a discounted strike payment when the contracts are identical in every material respect. If observed prices violate the relationship by more than the cost of trading and carrying the positions, a conversion or reversal may be available.
For options on futures, CME presents the equivalent form as:
c + K = F + p
Here F is the futures price. The futures version uses the same strike, expiration and underlying futures contract. Futures daily settlement means the financing of interim variation margin must still be considered even when the final payoff is locked.
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Carry adjustments that change the theoretical value
The simple stock equation assumes no dividends and an unrestricted ability to borrow or lend at the stated rate. Real instruments may require adjustments for:
- Cash dividends and their ex-dividend dates.
- The cost and availability of stock borrow for a short position.
- Interest earned on cash proceeds or paid on borrowed funds.
- Storage, insurance or other carrying costs for physical commodities.
- Contract-specific settlement, delivery and margin conventions.
These items belong in the parity estimate before a quote is called “cheap” or “expensive.” A mid-market theoretical value is not executable by itself; the relevant comparison is between the actual bid at which you can sell and the ask at which you can buy.
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Matching requirements
Before calculating a gap, match every attribute below. A mismatch can create genuine market exposure rather than arbitrage:
- Underlying security, index or futures contract.
- Strike price and expiration date and time.
- Contract multiplier and number of units.
- American or European exercise style.
- Physical delivery, cash settlement or futures assignment.
- Trading currency, trading hours and holiday calendar.
How a conversion works
A conversion is the options implementation of cash-and-carry:
- Buy the underlying stock or other deliverable asset.
- Buy a put with strike K and expiration T.
- Sell a call with the same strike and expiration.
At expiration, the stock plus the put minus the call is worth exactly K per share. If the stock finishes below the strike, the put lets you sell at K; if it finishes above the strike, the short call requires delivery at K. The terminal stock-price risk is therefore removed, provided the options are exercised or assigned according to their rules.
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Where the conversion profit comes from
The opening cash outlay per share is approximately S + put ask − call bid, before commissions and financing. Compare that executable amount with the present value of the strike after dividends, interest and any other carry. A conversion is attractive only when the guaranteed terminal receipt and all interim cash flows exceed the amount invested and every cost of maintaining the package.
For a stock that pays a dividend, the long stock receives the dividend, while the option parity calculation must reflect its amount and timing. A special dividend, uncertain dividend or early-exercise feature can make a seemingly small difference economically important.
Practical order construction
Use a broker’s qualified multi-leg order when available so the three legs can be executed as one package. If the legs are entered separately, the unfilled portion can leave you long or short stock or with an unhedged option. Confirm that the displayed net debit or credit uses executable prices, not theoretical mids, and that the order quantity reflects the contract multiplier.
How a reverse conversion (reversal) works
A reversal is the opposite package:
- Short the underlying stock or other asset.
- Buy a call with strike K and expiration T.
- Sell a put with the same strike and expiration.
The long call minus the short put minus the stock is worth −K at expiration. If the stock finishes above the strike, the call covers the short stock at K; if it finishes below the strike, the short put assigns stock at K. The position is therefore economically similar to borrowing the asset until expiration, but only if the short stock can remain open.
Why reversals are especially sensitive to borrow
A reversal needs shares to short. The stock may be hard to borrow, the borrow rate may change, or the lender may recall the shares before expiration. A borrow quote that is available for a small size or a single day does not establish that the position can be carried through assignment and settlement. Include the borrow fee, locate requirements, collateral rules and a contingency for a recall in the trade’s expected value.
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Dividends also affect this direction: the short seller normally owes the lender a payment in lieu of dividends. That obligation must be included with the put and call premiums and the interest earned on short-sale proceeds.
CME’s worked parity example
CME’s instructional example uses a futures price of 100, a 105 call priced at 2 and a 105 put that parity would value at 7. If the put can instead be sold at 8, the package is to sell the put, buy the call and sell the future. The option premium difference is 8 − 2 = 6. The short future is 5 points below the 105 strike, producing a 5-point offset when the option outcome is included. The model profit is therefore 1 point per futures unit, before multiplier and transaction costs.
| Futures settlement at expiration | Option outcome | Short-future outcome relative to 100 | Total result after the 6-point option premium difference |
|---|---|---|---|
| Below 105 | The short put is assigned; the long call expires | The future gains as the settlement falls, offsetting the put assignment | +1 point |
| Exactly 105 | Both options finish at the strike | The short future loses 5 points | +1 point |
| Above 105 | The long call gains; the short put expires | The short future loses as prices rise, offsetting the call gain | +1 point |
This is an idealized payoff illustration, not evidence of a current free-profit opportunity. The result assumes the stated prices can be executed, contracts match, funding and margin are handled, and no fees, slippage, borrow or assignment complications consume the one-point spread.
A step-by-step test for a real opportunity
- Identify the exact contract. Record the underlying, strike, expiration, multiplier, exercise style and settlement method for every leg.
- Model carry. Include financing, dividends, stock-borrow charges, storage or other contractual carry through expiration.
- Use executable quotes. Use the bid for a sale and the ask for a purchase. Replace stale or illiquid quotes with a conservative fill assumption.
- Calculate the complete package. Add commissions, exchange and clearing fees, taxes where applicable, spread costs, margin funding and expected assignment or exercise costs.
- Check capital and borrow. Confirm that the account can support stock margin, option margin, futures variation margin and any collateral requirement for the entire holding period. For a reversal, obtain a firm locate and a realistic borrow-rate estimate.
- Choose synchronized execution. Prefer a recognized conversion or reversal strategy order. If legs must be staged, define a maximum time and price exposure for the unhedged leg.
- Verify post-trade positions. Check that the stock quantity offsets the option contract delta at the package level, that all expirations match and that the broker booked the intended strategy.
- Monitor corporate and contract events. Track ex-dividend dates, expiration notices, early-assignment alerts, borrow changes, margin calls and futures delivery deadlines.
- Close or settle according to the rules. Do not assume automatic exercise, netting or cash settlement. Read the exchange and broker procedures for the specific contract.
Costs and risks that can erase the parity gap
| Cost or risk | How it affects a conversion | How it affects a reversal |
|---|---|---|
| Bid-ask spread and market impact | Raises the cost of buying stock and the put or lowers proceeds from selling the call | Raises the cost of buying the call and lowers proceeds from selling the put or stock |
| Funding and interest | Finances the long stock and option package until the terminal receipt | Determines the return on short-sale proceeds and the cost of margin |
| Dividends | Long stock receives dividends, but timing and amount must match the model | Short stock generally requires payments in lieu of dividends |
| Stock borrow | Usually not required for the stock leg, unless another hedge is short | Required; availability, fee changes and recalls can break the package |
| Margin and variation settlement | Stock and option margin can tie up capital | Short stock, options and futures margin can create additional cash calls |
| Assignment and exercise | Early call assignment can deliver stock before the planned date | Early put assignment can create or remove a stock position unexpectedly |
| Settlement and delivery | Physical delivery, cash settlement or option-to-future conversion may differ | Delivery deadlines and daily futures settlement can alter cash timing |
OIC cautions that borrowing restrictions and transaction costs can remove an apparent arbitrage. Interactive Brokers’ educational material also identifies early assignment, dividends, margin effects and transaction costs as execution considerations. Treat the theoretical spread as a starting calculation, not as net profit.
Settlement details that deserve special attention
American exercise and early assignment
American-style options can be exercised before expiration. A short call in a conversion may be assigned around a dividend, while a short put in a reversal may be assigned when the put is sufficiently in the money or its remaining time value is small. Assignment can change the stock position, financing and dividend exposure before the intended maturity. Have sufficient buying power and a written procedure for handling an assignment notice.
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Futures options and daily settlement
CME states that in-the-money futures options are settled according to put-call parity while taking the appropriate cost of carry into account. Futures themselves are marked to market daily. A package that has a locked expiration payoff can still require cash during the life of the trade if adverse daily price moves consume variation margin. The cost of that cash is part of the arbitrage calculation.
Multipliers and delivery rules
A one-point result in a CME example is multiplied by the contract’s stated unit. Equity options commonly represent a fixed number of shares, but corporate actions can change a contract’s deliverable. Confirm the current multiplier, deliverable and exercise notice process with the exchange and broker rather than assuming that every option represents the same number of shares.
Conversion versus reversal: choosing the direction
The direction is determined by which side of parity is expensive after carry adjustments. A conversion uses a long underlying and finances it with the option package; it is generally easier to analyze when the stock can be bought and carried without borrow constraints. A reversal uses a short underlying, so the trade is only viable when shares can be borrowed at a known, acceptable cost.
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Random freezes, missing sound and display glitches usually trace back to one bad driver. Find and replace yours safely.Free scan · under a minute| Decision question | Favors a conversion | Favors a reversal |
|---|---|---|
| Can the underlying be held? | Yes, with predictable funding and dividend treatment | No; the cash asset is expensive relative to the synthetic exposure |
| Is stock borrow available? | Borrow is irrelevant to the core long-stock package | A firm locate and fee schedule are available through expiration |
| Where is the executable mispricing? | Long stock plus long put is cheap relative to selling the call | Long call plus short put is cheap relative to shorting the stock |
| What can force an early unwind? | Funding limits, dividend events or call assignment | Borrow recall, rising borrow fees, margin calls or put assignment |
When the trade is not truly risk-free
In textbook arbitrage, identical cash flows are bought and sold at different prices, so the difference is locked. In a live options account, “risk-free” applies only after every cash flow is contractually matched and operationally funded. A quote can look out of line because one leg is stale, because the stock is hard to borrow, because a dividend is mis-modeled or because the settlement conventions differ.
The correct standard is stricter: the net spread must remain positive after executable prices, financing, dividends, borrow, commissions, exchange fees, margin funding, expected assignment costs and a reserve for operational errors. If a one-point theoretical edge disappears after those deductions, there is no arbitrage to trade. If the edge survives, the remaining exposure is usually implementation risk—execution, funding, borrow, assignment or settlement—not a forecast of the stock’s direction.
Quick Recap
Pre-trade checklist
- Underlying, strike, expiration and multiplier match exactly.
- Exercise style and settlement method are documented.
- Parity is adjusted for interest, dividends and borrow or other carry.
- Every leg is priced at an executable bid or ask.
- Commissions, exchange fees, spread, margin and funding are included.
- Stock locate, borrow rate and recall terms are confirmed for a reversal.
- Account buying power covers assignment, delivery and variation-margin scenarios.
- Dividend, expiration and exercise-notice dates are on the monitoring calendar.
- The broker’s procedure for multi-leg exercise, assignment and settlement is understood.
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