Updated for the 2026-2027 CFA® Level I curriculum.
Put-call forward parity links European call and put prices to a forward contract on the same underlying. It replaces the spot price used in standard put-call parity with the present value of the forward price. This matters because many exam questions give you a forward price rather than a spot price. After this note, you should be able to set up the parity equation, solve for a missing price, and identify when a mispricing creates an arbitrage opportunity.
Quick Answer
Put-call forward parity states that a European call price minus a European put price, on the same underlying, strike, and expiration, equals the present value of the difference between the forward price and the strike.
The formula is . It follows from standard put-call parity by substituting the present value of the forward price for the spot price. Use it to find a missing option price or spot mispricing.
Key Takeaways About Put-Call Forward Parity for European Options
Put-call forward parity connects a call price, a put price, and a forward price on the same underlying, strike, and expiration.
The relationship is
is the forward price agreed today for delivery at time . is the shared strike price.
The formula comes from substituting the present value of the forward price for the spot price in standard put-call parity.
A long call plus a short put, matched on strike and expiration, replicates a long forward position.
If quoted prices do not satisfy the equation, an arbitrage opportunity exists.
A common error is discounting only one side of the equation, the strike or the forward price, instead of both.
What You Need to Know for CFA Level I
Know the put-call forward parity formula and what each variable represents.
Be able to derive the relationship from standard put-call parity by substitution.
Recognize that a long call and short put with matching terms replicate a forward payoff.
Use the formula to solve for a missing call price, put price, or forward price.
Identify when quoted prices violate parity and explain the resulting arbitrage.
Distinguish this forward-based relationship from the spot-based put-call parity formula.
What Is Put-Call Forward Parity?
Put-call forward parity is a pricing relationship between a European call, a European put, and a forward contract that share the same underlying asset, strike price, and expiration date. A long call combined with a short put produces the same payoff as a long forward contract on the underlying.
This is a variation of standard put-call parity. Standard parity uses the spot price of the underlying. Forward parity uses the forward price instead. Both describe the same economic relationship, viewed from different starting points.
Put-Call Forward Parity Relationship
Where:
= price of the European call today
= price of the European put today
= forward price set today for delivery at time
= strike price shared by the call and put
= risk-free rate
= time to expiration, in years
= current spot price of the underlying asset
= price of the underlying asset at expiration
The right side is the present value of the difference between the forward price and the strike. This present value equals the difference between the call price and the put price.
How It Connects to Put-Call Parity
Standard put-call parity:
The forward price relates to the spot price through , assuming no other carry costs on the underlying. Rearranged, .
Substitute this into standard parity:
Rearrange:
This is put-call forward parity. Both relationships describe the same portfolio equivalence. Forward parity is more direct when the forward price is quoted and the spot price is not needed separately.
Synthetic Forward From Options
A long call and a short put, matched on strike and expiration, replicate a long forward position.
Position | If | If |
|---|---|---|
Long call | 0 | |
Short put | 0 | |
Combined |
The combined payoff, , matches the payoff of a long forward with a forward price equal to . This is why the option combination and the forward price consistently.
Using Forward Parity to Find a Missing Price
Given three of the four prices, along with the risk-free rate and time, you can solve for the fourth.
Worked Example
Setup. A stock has European call and put options expiring in one year, both with a strike price of $50. The one-year forward price on the stock is $53. The risk-free rate is 4%. The put trades at $2.10. Find the call price implied by put-call forward parity.
Step 1. Apply the formula.
Step 2. Substitute values.
Given the put price, forward price, and strike, the call should trade at $4.98 for parity to hold. If the market price differs, the options and the forward are mispriced relative to each other.
Arbitrage Interpretation
If market prices do not satisfy the parity equation, an arbitrage opportunity exists. A trader buys the cheaper side of the equation and sells the more expensive side, locking in a profit before transaction costs.
If is greater than , the call and put combination is priced too high relative to the forward. Selling the call, buying the put, and taking the offsetting forward position captures the mispricing. The reverse trade applies if the combination is priced too low.
Common Exam Traps
Using options with different strikes or maturities. Put-call forward parity only holds when the call, put, and forward reference the same strike and expiration. Mismatched terms break the relationship.
Confusing spot parity with forward parity. Spot parity uses directly. Forward parity uses the present value of . Mixing the two in one equation produces a wrong answer.
Forgetting to discount both the forward price and the strike. Both and must be brought to present value. Discounting only one side overstates or understates the price difference.
Treating the forward price as the forward contract's current value. is the price agreed for future delivery. It is not the value of the forward contract today, which is zero for both parties at initiation.
Practice Questions
A European call and put on the same stock share a strike price of $40 and expire in one year. The one-year forward price on the stock is $41.05. The risk-free rate is 5%. The call trades at $3.50.
Using put-call forward parity, the put price consistent with this data is closest to:
$2.50
$3.50
$4.55
Correct Answer: A
Reasoning.
Option B: $3.50 simply repeats the call price and ignores the forward-strike adjustment entirely.
Option C: $4.55 adds the adjustment to the call price instead of subtracting it, reversing the formula.
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FAQs About Put-Call Forward Parity for European Options
Why use forward parity instead of spot put-call parity?
Forward parity is useful when the forward price is quoted directly and you do not need the spot price separately. It expresses the same relationship without an extra conversion step.
Does put-call forward parity apply to American options?
No. American options can be exercised early, which breaks the fixed pricing relationship. Put-call forward parity applies only to European options, which can only be exercised at expiration.