# Conversion and Reversal Arbitrage: Put-Call Parity in Practice

Derive conversion and reversal positions from put-call parity, verify their fixed expiration cash flow, and account for financing, dividends, stock borrow, and assignment.

Canonical: https://wiki.fcontext.com/options/conversion-reversal-arbitrage/
Fact checked: 2026-07-22

> For educational purposes only; not investment advice.

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## Direct answer

A **conversion** combines long stock, a long put, and a short call with the same strike and expiration. A **reversal** uses the opposite positions: short stock, long call, and short put. They compare actual stock with synthetic stock through put-call parity.

For European options on a non-dividend-paying stock:

`C − P = S − K e^(−rT)`

A price discrepancy can imply a fixed theoretical expiration cash flow, but “arbitrage” is conditional on simultaneous executable prices, financing, dividends, borrow availability, exercise terms, margin, taxes, and fees.

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## Why the expiration value is fixed

The conversion expiration value is:

`Sₜ + max(K−Sₜ,0) − max(Sₜ−K,0) = K`

Below `K`, the put raises stock value to `K`; above `K`, the short call gives away the amount above `K`. The package therefore pays `K` at expiration before financing and carrying adjustments. Its fair present cost is the present value of that payment, adjusted for dividends and contract features.

The reversal is the exact opposite and pays `−K` at expiration. It receives cash initially and requires `K` at maturity. A conversion is attractive only if its all-in executable cost is below the correctly adjusted present value of `K`; a reversal is attractive only if its net proceeds exceed that value.

American exercise breaks the clean hold-to-expiration path. Known dividends alter parity, while uncertain dividends create estimation risk. A short-stock reversal also requires a locate and continuing borrow, and may owe dividends to the lender.

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## A theoretical conversion discrepancy

Assume European options, no dividends, one year to expiration, continuous risk-free rate `r=5%`, stock `S=100`, and strike `K=100`. Then:

`PV(K) = 100e^(−0.05) ≈ 95.12`

Suppose the executable call price is `8.00` and put price is `2.00`. The conversion costs:

`S + P − C = 100 + 2 − 8 = 94.00`

It pays `100` at expiration, so its theoretical present-value discount is `95.12−94.00=1.12` per share. If `94.00` is borrowed at the same continuous 5% rate, repayment is `94e^0.05≈98.82`, leaving theoretical gross expiration profit of about `1.18` per share, or `$118` for a 100-share package.

This is not a retail profit promise. Bid-ask execution, commissions, margin rates, dividends, early assignment, stock and option settlement, taxes, and rejected or partial legs can exceed the discrepancy.

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## Verification and execution checklist

- Use the same underlying, strike, expiration, multiplier, deliverable, and exercise style for call and put.
- Snapshot executable stock, call, and put prices at one instant; stale last prices do not form an arbitrage.
- Include expected dividends and their timing, not merely the current dividend yield.
- Use the account's marginal borrowing or lending rate, not an abstract risk-free rate.
- For reversals, confirm locate, borrow fee, collateral terms, recall risk, and payments in lieu of dividends.
- Submit linked orders where available and size every leg to the same share-equivalent quantity.
- Model early exercise of short American options, especially deep-in-the-money calls before ex-dividend dates and puts when carrying value changes.
- Reconcile assignment, exercise, and stock settlement promptly; timing mismatches can require substantial cash or shares.
- Calculate after-tax, after-fee return on committed capital. A positive parity residual alone is insufficient.

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## Common misconceptions

- “Conversion is directionally long stock.” The put and short call neutralize the stock's expiration direction under the stated terms.
- “Any parity difference is free money.” Only simultaneous executable prices after every carrying cost matter.
- “A reversal does not need stock borrow because options offset it.” The short stock still requires delivery, borrow, and margin.
- “Implied volatility drives the locked payoff.” IV affects leg prices, but the matched expiration identity comes from cash flows.
- “The package can always wait until expiration.” American assignment, borrow recall, broker controls, and corporate actions can interrupt it.
- “Theoretical profit equals account profit.” Financing asymmetry, taxes, fees, and settlement timing can reverse the result.

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## Related topics

- [Put-Call Parity](/options/put-call-parity/)
- [Synthetic Stock](/options/synthetic-stock/)
- [Assignment Risk](/options/assignment-risk/)
- [Stock Borrow Fees](/stocks/stock-borrow-fees/)

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## Authoritative sources

- [Put/Call Parity](https://prd-web.optionseducation.org/advancedconcepts/put-call-parity) - Options Industry Council
- [Key Points About Regulation SHO](https://www.sec.gov/investor/pubs/regsho.htm) - U.S. Securities and Exchange Commission
- [Characteristics and Risks of Standardized Options](https://www.theocc.com/company-information/documents-and-archives/options-disclosure-document) - Options Clearing Corporation