Conversion at a glance
| Construction | Buy 100 shares, buy 1 at the money put, and sell 1 at the money call at the same strike, both options in the front month expiration. |
|---|---|
| Outlook | Market neutral |
| Volatility view | IV neutral |
| Max profit | Strike minus stock purchase price plus call premium minus put premium, times 100, plus dividends received, minus financing costs. |
| Max loss | The same locked amount when it is negative: if the stock price plus the put costs more than the strike plus the call premium and carry, you lose that difference times 100. |
| Breakeven | There is no price breakeven, since the result does not depend on where the stock finishes. |
| Experience level | Advanced |
| Also called | Conversion arbitrage |
How a conversion works
A conversion, or conversion arbitrage, pairs long stock with a synthetic short: the long put and short call at the same strike together behave like short stock. The two cancel, so your shares will be delivered at the strike at expiration through either call assignment or put exercise. Your outcome is set on day one: you receive the strike price at expiration plus any dividends, and you paid the stock price plus the put minus the call, plus financing. Market makers use conversions to manage inventory and trade put call parity.
At expiration the payoff is a flat line. If the stock is above the strike, your short call is assigned and you deliver the shares. If it is below, you exercise the put and deliver the shares. Either way the position closes at the strike. The locked result equals the strike minus the stock price plus the call premium minus the put premium. Carrying costs come off that amount: interest on the cash used to buy the shares, minus any dividends received before expiration.
Before expiration the conversion has almost no delta, gamma, or vega, because the synthetic short offsets the stock. What it does have is exposure to interest rates and dividends. If you finance the shares at a floating rate and rates rise, your carrying cost increases while the locked value does not, and a dividend cut lowers income the trade was counting on. For American options, put call parity is a range rather than an exact equation, which is why conversion prices can drift within bounds without any arbitrage.
Conversion example with real numbers
With the stock at $100, implied volatility at 30%, a 4.1% risk free rate and no dividend, you would buy 100 shares at $100.00, buy 1 100 put (32 days) at $3.39, sell 1 100 call (32 days) at $3.73. That is a net debit of $9,966. At expiration a maximum profit of $34.00 and a maximum loss of $34.00. The lognormal chance of profit is 100%.
These are theoretical American option prices from the Bjerksund and Stensland model, not live quotes. Load any ticker in the conversion calculator above to run the same math on real market prices.
When to use a conversion
- The call is priced high relative to the put, so the locked value exceeds your carrying cost.
- You want to lock in the value of an existing long stock position until expiration without selling the shares.
- You are studying put call parity and want to see how carry, dividends and strikes affect fair value.
- You expect the dividend to be paid as scheduled and want to capture it alongside the option pricing.
Max profit, max loss and breakeven
Maximum profit
Strike minus stock purchase price plus call premium minus put premium, times 100, plus dividends received, minus financing costs. The amount is fixed at entry as long as no leg is exercised or assigned early.
Maximum loss
The same locked amount when it is negative: if the stock price plus the put costs more than the strike plus the call premium and carry, you lose that difference times 100. Further losses can come from early assignment that removes the dividend, dividend cuts, rate changes, or pin risk.
Breakeven
There is no price breakeven, since the result does not depend on where the stock finishes. The trade breaks even when the call premium minus the put premium equals the stock price minus the strike plus net carrying cost (financing minus dividends).
Conversion Greeks
- Delta: Delta is close to zero, because the 100 shares are offset by the short call and long put.
- Gamma: Gamma is close to zero, since the long put and short call at the same strike carry nearly equal gamma.
- Theta: Theta is small and mostly reflects carry, meaning interest on the stock position and dividends rather than option decay.
- Vega: Vega is close to zero, although the early exercise premium on American puts can leave a small residual exposure.
See the live numbers for your position in the Greeks tab of the calculator, or explore a single option in the options Greeks calculator.
Early exercise and assignment risk
Dividend risk is the classic hazard for a conversion. Conversions are priced assuming you hold the shares through the ex dividend date and collect the payout. But if the stock rallies and the short call goes deep in the money, the call holder can exercise on the trading day before the ex date whenever the dividend is larger than the call's remaining time value. Your shares are delivered early, you receive the strike, and the dividend you counted on disappears from the trade. That loss can erase the small edge that made the conversion worthwhile.
Early assignment without a dividend is less harmful: you receive the strike sooner than planned and keep the long put, which may still have some value. Pin risk is the other American option concern. If the stock closes right at the strike on expiration day, you may not know whether your short call will be assigned. If you exercise the put and the call is also assigned, you end up short 100 shares; if you do neither and the call is not assigned, you still own the stock. Closing before the final session removes that uncertainty.
The calculator's Early exercise risk tab flags short legs that are likely to be assigned. For a single option, use the early exercise calculator or read how early exercise and assignment work.
Pros and cons
Pros
- Locked in value with almost no directional risk.
- Helps reveal mispricing between calls, puts, and stock.
- Converts an existing long stock holding into a fixed value position until expiration.
- Simple, flat payoff at expiration.
Cons
- Edges are very small, so commissions and bid ask spreads can erase them.
- Early assignment of the call can remove the dividend the trade relied on.
- Pin risk at expiration can leave an unexpected stock position.
- Ties up the capital for 100 shares to earn a small return.
How to manage a conversion
- Price the trade with your actual financing rate and the expected dividend before entering.
- Watch the short call's time value ahead of each ex dividend date and plan for assignment.
- Close the position before expiration if the stock is near the strike to avoid pin risk.
- Enter all three legs at once with a combined limit price.
Conversion FAQ
What is a conversion in options?
A conversion is an arbitrage position made of long stock, a long put, and a short call at the same strike and expiration. The options form a synthetic short that offsets the shares, so the value at expiration is fixed at the strike. The profit or loss is set at entry by the option prices, the stock price, and carrying costs.
Is a conversion risk free?
A conversion is not completely risk free, even though its payoff at expiration is fixed. With American options, early assignment before an ex dividend date can remove expected dividend income, and pin risk can leave an unexpected stock position. Interest rate changes and dividend cuts can also hurt.
What is the difference between a conversion and a reversal?
A conversion is long stock with a synthetic short, while a reversal is short stock with a synthetic long. A conversion profits when calls are rich relative to puts, and a reversal profits when puts are rich relative to calls. Conversions mainly worry about losing dividends to early call assignment, while reversals worry about early put assignment and borrow costs.
Why do market makers use conversions?
Market makers use conversions to lay off directional risk from options they trade with customers. If they sell calls, buying stock and buying puts turns that exposure into a conversion with a locked value. It also lets them trade the relationship between call and put prices described by put call parity.
Related strategies
Reversal
A reversal, also called a reverse conversion, is a market neutral arbitrage position that shorts 100 shares, sells an at the money put, and buys an at the money call at the same strike, locking in a fixed value at expiration.
Box Spread
A box spread is a four leg options position that combines a bull call spread and a bear put spread on the same two strikes, so it is worth exactly the distance between the strikes at expiration.
Synthetic Short Stock
Synthetic short stock is a short call and a long put at the same strike and expiration, a combination that behaves almost exactly like being short 100 shares.
Collar
A collar is a position that owns 100 shares of stock, buys a protective put below the market and sells a covered call above it.
Educational tool, not financial advice. Calculations are theoretical and depend on your inputs; real fills, fees, early assignment and dividends can change results. Options involve risk and are not suitable for every investor.