Conversion (Options Arbitrage)
A Conversion is a three-leg options arbitrage strategy in which a trader who owns stock sells a call and buys a put at the same strike and expiration, creating a synthetic short position that offsets the long stock and locks in a risk-free profit when mispricing exists.
The conversion trade exploits violations of put-call parity, a fundamental options pricing relationship that states the price of a call and the price of a put with the same strike and expiration must maintain a specific mathematical relationship relative to the stock price, strike, time, and interest rates.
Put-call parity states that: Call - Put = Stock - Present Value of Strike. When this relationship breaks down — typically due to short-term supply-demand imbalances, dividend uncertainty, or financing rate changes — a risk-free profit can be captured through the conversion.
The conversion is executed as follows: own 100 shares of stock, sell one at-the-money call, and buy one at-the-money put with the same expiration. The combined position of long stock, short call, and long put creates a completely hedged outcome. If the stock rises above the strike, the short call is assigned and the stock is delivered at the strike price. If the stock falls below the strike, the long put is exercised and the stock is also delivered at the strike price. Either way, the exit price is fixed at the strike regardless of market movement.
The profit in a conversion comes from the difference between what the trader receives for this locked-in outcome versus what they paid. If the put-call parity is violated and calls are overpriced relative to puts, the conversion generates an arbitrage profit equal to the mispricing minus transaction costs.
In practice, conversions are executed almost exclusively by market makers and institutional desks. These professionals have the technology to detect parity violations in milliseconds and the low transaction costs to make thin arbitrage margins worthwhile. For retail traders, commissions and bid-ask spreads typically eliminate any edge before the trade can be executed.
Conversions are most likely to be profitable around dividend ex-dates when the implied dividend embedded in put prices diverges from the actual announced dividend, creating temporary put-call parity violations that sophisticated traders can exploit.