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Put-Call Parity Checker

Check put-call parity relationship between put and call options to identify arbitrage opportunities and verify option pricing.

Put-Call Parity Checker

Check put-call parity relationship between put and call options to identify arbitrage opportunities and verify option pricing.

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Guide

Understanding put-call parity and option pricing relationships

  • Put-Call Parity: Call + PV(Strike) = Put + Spot. This relationship must hold for European options to prevent arbitrage opportunities.
  • PV(Strike) = Strike Price / (1 + r)^t, where r is risk-free interest rate and t is time to expiration in years.
  • If parity is violated (large difference), arbitrage opportunity exists. Buy the undervalued side and sell the overvalued side to lock in risk-free profit.
  • Put-call parity applies to European options (exercisable only at expiration). American options may deviate due to early exercise opportunities.
  • Factors affecting parity include transaction costs, dividends, early exercise (American options), and market frictions. Small differences may be due to these factors.

Frequently Asked Questions

Put-call parity, option pricing, and arbitrage opportunities

What is put-call parity?

Put-call parity is a relationship between put and call options with the same strike and expiration: Call + PV(Strike) = Put + Spot. It must hold to prevent arbitrage.

Why is put-call parity important?

Put-call parity ensures option prices are consistent. Violations indicate mispricing and arbitrage opportunities, allowing risk-free profit by buying the undervalued side and selling the overvalued side.

How is put-call parity calculated?

Put-Call Parity: Call + PV(Strike) = Put + Spot, where PV(Strike) = Strike / (1 + r)^t. If both sides are equal (within small tolerance), parity holds.

Does put-call parity apply to American options?

Put-call parity applies strictly to European options (exercisable only at expiration). American options may deviate due to early exercise opportunities, but the relationship is approximately true.

What if put-call parity is violated?

If parity is violated (large difference), arbitrage opportunity exists. Execute the arbitrage strategy: buy the undervalued side and sell the overvalued side to lock in risk-free profit.

How do dividends affect put-call parity?

Dividends affect put-call parity by reducing the spot price (adjusted for present value of dividends). Modified parity: Call + PV(Strike) = Put + Spot - PV(Dividends).

What is a reasonable tolerance for put-call parity?

Small differences (<$0.01) are acceptable due to transaction costs and market frictions. Large differences (>$0.10) indicate potential arbitrage opportunities or significant mispricing.

Can I use put-call parity to price options?

Yes. If you know three of the four values (call price, put price, spot price, strike price), you can calculate the fourth using put-call parity, assuming parity holds.

How does interest rate affect put-call parity?

Higher interest rates increase PV(Strike), making the left side larger. This means calls should be more expensive relative to puts, all else equal, to maintain parity.

What are transaction costs in put-call parity arbitrage?

Transaction costs (commissions, spreads, borrowing costs) reduce arbitrage profits. Ensure the difference exceeds transaction costs before executing arbitrage strategies.

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Put-Call Parity Checker

Check put-call parity relationship between put and call options to identify arbitrage opportunities and verify option pricing.

How to use Put-Call Parity Checker

Step-by-step guide to using the Put-Call Parity Checker:

  1. Enter your values. Input the required values in the calculator form
  2. Calculate. The calculator will automatically compute and display your results
  3. Review results. Review the calculated results and any additional information provided

Frequently asked questions

How do I use the Put-Call Parity Checker?

Simply enter your values in the input fields and the calculator will automatically compute the results. The Put-Call Parity Checker is designed to be user-friendly and provide instant calculations.

Is the Put-Call Parity Checker free to use?

Yes, the Put-Call Parity Checker is completely free to use. No registration or payment is required.

Can I use this calculator on mobile devices?

Yes, the Put-Call Parity Checker is fully responsive and works perfectly on mobile phones, tablets, and desktop computers.

Are the results from Put-Call Parity Checker accurate?

Yes, our calculators use standard formulas and are regularly tested for accuracy. However, results should be used for informational purposes and not as a substitute for professional advice.