📊 Put-Call Parity Calculator

Put-call parity says a call plus the present value of the strike must equal a put plus the stock, for European options on a non-dividend stock. When the two sides differ, one side is mispriced relative to the other, which is the starting point of conversion and reversal arbitrage. This calculator runs the check and tells you which side is rich.

For retail traders the practical use is simpler than arbitrage: parity is a sanity check on quotes. If your broker shows a call/put pair violating parity by a wide margin, something is off: stale quotes, a wide spread, or an upcoming dividend you forgot about.

How to Use This Calculator

Enter the stock price, the strike both options share, the call ask and put ask, the risk-free rate, and the time to expiry in years. Use options on the same expiry and the same strike; parity only applies to matched pairs.

The Put-Call Parity Formula

The left side is a fiduciary call: a call plus cash equal to the discounted strike, which guarantees you can buy the stock at expiry. The right side is a protective put: the stock plus a put guarding it. Both positions end with the stock in hand at expiry, so in an efficient market they must cost the same today. The calculator uses continuous discounting, K x e^(-rT), which matches market convention.

Rearranged, parity creates synthetic positions: a synthetic long stock equals call minus put plus discounted strike. Market makers use these identities constantly to keep related quotes in line, which is why retail traders rarely find clean violations.

Worked Example

Stock at $100, $100 strike, 1 year to expiry, 5 percent risk-free rate. Call quoted at $8, put at $6. PV of strike = $100 x e^(-0.05) = $95.12. Left side = $8 + $95.12 = $103.12. Right side = $6 + $100 = $106.00. Gap = -$2.88. The put side is rich by $2.88: the put is expensive relative to the call, or the call is cheap.

A textbook arbitrage would sell the rich side and buy the cheap side: sell the put, sell the stock, buy the call, and invest the discounted strike. In practice the $2.88 shrinks fast once you use real bid-ask spreads instead of midpoints, add commissions, and post margin. Treat small gaps as information, not free money.

Why Parity Breaks in Real Markets

Nine times out of ten, an apparent violation is one of these frictions, not an opportunity. Dividends are the most overlooked: a $2 dividend before expiry explains a $2 gap completely. Always check the ex-dividend date before concluding anything.

A Retail Trader’s Practical Checklist

Use parity as a quote-quality filter. Before trading a spread, check that the call and put at each strike roughly satisfy parity; a leg that violates it badly deserves a second look at its quote. When rolling positions, parity tells you whether the new expiry’s pricing is consistent with the old. And when a strategy’s breakeven looks too good, parity is often the identity that reveals the hidden cost. For position sizing around any options trade, our position sizing thinking pairs with the risk-reward math most traders already use.

One caution: this calculator, like the formula, ignores dividends and assumes European exercise. Most US equity options are American-style, so treat the verdict as a signal to investigate, not a trade ticket. Estimates for planning only, not financial advice.

The Arbitrage Trade, Step by Step

When the call side is rich by $2.88, the textbook conversion sells the call, buys the put, buys the stock, and borrows the present value of the strike. At expiry the positions collapse: if the stock is above the strike, the short call assigns against the long stock; below, the long put is exercised to sell it. Either way the trader ends flat, keeps the $2.88 minus costs, and the position is hedged the entire time. The reversal does the mirror image when the put side is rich.

Professionals run these automatically, which is why the gaps close in seconds on liquid names. The retail lesson is not to compete but to understand what the machine is doing: every conversion lifts the cheap side and presses the rich side until parity returns. When you see a persistent gap on an illiquid option, the right response is usually to avoid that strike, not to attack it. The edge belongs to whoever pays the least to trade, and that is never the retail account.

Parity and the Volatility Smile

Put-call parity holds regardless of volatility assumptions, which makes it the perfect diagnostic when option prices look strange. If calls and puts at the same strike imply wildly different volatilities, parity tells you which one is mispriced relative to the other rather than to some model. Market makers keep the two legs consistent; when they are not, the cause is usually a dividend, a borrow fee, or a stale quote, in that order.

For students of options, parity is also the fastest route to intuition about synthetics. Long stock equals long call plus short put plus cash: rearrange the formula and every synthetic position drops out. Once you can build synthetic stock, you can build synthetic anything, and spreads stop being memorized recipes and start being legible structures. Learn parity deeply and the rest of options math gets easier, because so much of it is parity in disguise.

Estimates for planning only, not financial advice.