Conversions And Reversals

Put-call parity says a call, a put, and the underlying stock (with the same strike and expiry) must price consistently with each other — specifically $C - P = S - K e^{-rT}$. A conversion exploits a violation where the call is overpriced relative to the put: buy the stock, sell the call, and buy the put (all at the same strike), which locks in the riskless side of the mispricing regardless of where the stock ends up, since the long stock plus long put plus short call payoff is fixed at expiry. A reversal is the mirror trade for the opposite mispricing: short the stock, buy the call, sell the put.

Because both legs are fully hedged, the position's payoff at expiry is a known, fixed cash amount — the trade only makes money if that locked-in amount exceeds the net cost of putting it on, including financing and transaction costs. Market makers run these constantly as a form of risk-free inventory management: if their quoted call is trading rich relative to the matching put, a conversion captures the edge without taking on any directional stock risk.

For example, with stock at $100, a 100-strike call priced at $6 and put at $3 with the parity-implied put price actually $4, buying the put, selling the call, and buying the stock locks in a $1 riskless profit (per share) once financing costs are subtracted.