Put-Call Parity Calculator

✖Spot Price of Underlying Asset refers to its current market price for immediate delivery or settlement.ⓘ Spot Price of Underlying Asset [S_t]			+10% -10%
✖Put Option Price represents the cost paid by the option buyer to obtain the right, but not the obligation, to sell the underlying asset at a specified strike price.ⓘ Put Option Price [p_t]			+10% -10%
✖Strike Price is the pre-determined price at which the buyer and seller of an option agree on a contract or exercise a valid and unexpired option.ⓘ Strike Price [X_s]			+10% -10%
✖Risk-Free Rate of Return is the interest rate an investor can expect to earn on an investment that carries zero risk.ⓘ Risk-Free Rate of Return [R_f]			+10% -10%
✖No. of Months is the period in which the call/put option is valid before expiration.ⓘ No. of Months [n_m]			+10% -10%

✖Call Option Price is the amount paid by the option buyer to acquire the right, but not the obligation, to purchase the underlying asset at a predetermined strike price.ⓘ Put-Call Parity [c_t]

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Formula

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Put-Call Parity

Formula

`"c"_{"t"} = "S"_{"t"}+"p"_{"t"}-(("X"_{"s"})/((1+("R"_{"f"}/100))^("n"_{"m"}/12)))`

Example

`"7.292972"="53"+"4"-(("50.1")/((1+("3.2"/100))^("3"/12)))`

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Put-Call Parity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Call Option Price = Spot Price of Underlying Asset+Put Option Price-((Strike Price)/((1+(Risk-Free Rate of Return/100))^(No. of Months/12)))
c_t = S_t+p_t-((X_s)/((1+(R_f/100))^(n_m/12)))
This formula uses 6 Variables

Variables Used

Call Option Price - Call Option Price is the amount paid by the option buyer to acquire the right, but not the obligation, to purchase the underlying asset at a predetermined strike price.
Spot Price of Underlying Asset - Spot Price of Underlying Asset refers to its current market price for immediate delivery or settlement.
Put Option Price - Put Option Price represents the cost paid by the option buyer to obtain the right, but not the obligation, to sell the underlying asset at a specified strike price.
Strike Price - Strike Price is the pre-determined price at which the buyer and seller of an option agree on a contract or exercise a valid and unexpired option.
Risk-Free Rate of Return - Risk-Free Rate of Return is the interest rate an investor can expect to earn on an investment that carries zero risk.
No. of Months - No. of Months is the period in which the call/put option is valid before expiration.

STEP 1: Convert Input(s) to Base Unit

Spot Price of Underlying Asset: 53 --> No Conversion Required
Put Option Price: 4 --> No Conversion Required
Strike Price: 50.1 --> No Conversion Required
Risk-Free Rate of Return: 3.2 --> No Conversion Required
No. of Months: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

c_t = S_t+p_t-((X_s)/((1+(R_f/100))^(n_m/12))) --> 53+4-((50.1)/((1+(3.2/100))^(3/12)))

Evaluating ... ...

c_t = 7.29297151436622

STEP 3: Convert Result to Output's Unit

7.29297151436622 --> No Conversion Required

FINAL ANSWER

7.29297151436622 ≈ 7.292972 <-- Call Option Price

(Calculation completed in 00.004 seconds)

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Created by Keerthika Bathula

Indian Institute of Technology, Indian School of mines, Dhanbad (IIT ISM Dhanbad), Dhanbad

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< 13 International Finance Calculators

FRA Payoff ( Long Position )

Go FRA Payoff = Notional Principal*(((Underlying Rate at Expiration-Forward Contract Rate)*(Number of Days in Underlying Rate/360))/(1+(Underlying Rate at Expiration*(Number of Days in Underlying Rate/360))))

Put-Call Parity

Go Call Option Price = Spot Price of Underlying Asset+Put Option Price-((Strike Price)/((1+(Risk-Free Rate of Return/100))^(No. of Months/12)))

Option Premium

Go Option Premium = ((Share Option Warrant/Number of Securities Per Option Warrant)+(Purchase Price*100/Price Security-100))

Balance of Financial Account

Go Balance of Financial Account = Net Direct Investment+Net Portfolio Investment+Asset Funding+Errors and Omissions

Annualised Forward Premium

Go Annualised Forward Premium = (((Forward Rate-Spot Rate)/Spot Rate)*(360/No. of Days))*100

Balance of Capital Account

Go Balance of Capital Account = Surpluses or Deficits of Net Non-Produced+Non-Financial Assets+Net Capital Transfers

Current Account Balance

Go Current Account Balance = Exports-Imports+Net Income Abroad+Net Current Transfers

Uncovered Interest Rate Parity

Go Expected Future Spot Rate = Current Spot Exchange Rate*((1+Domestic Interest Rate)/(1+Foreign Interest Rate))

Covered Interest Rate Parity

Go Forward Exchange Rate = (Current Spot Exchange Rate)*((1+Foreign Interest Rate)/(1+Domestic Interest Rate))

International Fisher Effect using Interest Rates

Go Change in Exchange Rate = ((Domestic Interest Rate-Foreign Interest Rate)/(1+Foreign Interest Rate))

Relative Strength Index

Go Relative Strength Index = 100-(100/(1+(Average Gain during Up Period/Average Loss during Down Period)))

Bid Ask Spread

Go Bid Ask Spread = ((Ask Price-Bid Price)/Ask Price)*100

International Fischer Effect using Spot Rates

Go Change in Exchange Rate = (Current Spot Exchange Rate/Spot Rate in Future)-1

Put-Call Parity Formula

Call Option Price = Spot Price of Underlying Asset+Put Option Price-((Strike Price)/((1+(Risk-Free Rate of Return/100))^(No. of Months/12)))
c_t = S_t+p_t-((X_s)/((1+(R_f/100))^(n_m/12)))

What is Put-Call Parity?

Put-call parity is an important concept in options pricing which shows how the prices of puts, calls, and the underlying asset must be consistent with one another. This equation establishes a relationship between the price of a call and put option which have the same underlying asset. For this relationship to work, the call and put option must have an identical expiration date and strike price. The put-call parity relationship shows that a portfolio consisting of a long call option and a short put option should be equal to a forward contract with the same underlying asset, expiration, and strike price. This equation can be rearranged to show several alternative ways of viewing this relationship.The put-call parity theory is important to understand because this relationship must hold in theory. With European put and calls, if this relationship does not hold, then that leaves an opportunity for arbitrage.

How to Calculate Put-Call Parity?

Put-Call Parity calculator uses Call Option Price = Spot Price of Underlying Asset+Put Option Price-((Strike Price)/((1+(Risk-Free Rate of Return/100))^(No. of Months/12))) to calculate the Call Option Price, The Put-Call Parity is an important concept in options pricing which shows how the prices of puts, calls, and the underlying asset must be consistent with one another. Call Option Price is denoted by c_t symbol.

How to calculate Put-Call Parity using this online calculator? To use this online calculator for Put-Call Parity, enter Spot Price of Underlying Asset (S_t), Put Option Price (p_t), Strike Price (X_s), Risk-Free Rate of Return (R_f) & No. of Months (n_m) and hit the calculate button. Here is how the Put-Call Parity calculation can be explained with given input values -> 7.292972 = 53+4-((50.1)/((1+(3.2/100))^(3/12))).

FAQ

What is Put-Call Parity?

The Put-Call Parity is an important concept in options pricing which shows how the prices of puts, calls, and the underlying asset must be consistent with one another and is represented as c_t = S_t+p_t-((X_s)/((1+(R_f/100))^(n_m/12))) or Call Option Price = Spot Price of Underlying Asset+Put Option Price-((Strike Price)/((1+(Risk-Free Rate of Return/100))^(No. of Months/12))). Spot Price of Underlying Asset refers to its current market price for immediate delivery or settlement, Put Option Price represents the cost paid by the option buyer to obtain the right, but not the obligation, to sell the underlying asset at a specified strike price, Strike Price is the pre-determined price at which the buyer and seller of an option agree on a contract or exercise a valid and unexpired option, Risk-Free Rate of Return is the interest rate an investor can expect to earn on an investment that carries zero risk & No. of Months is the period in which the call/put option is valid before expiration.

How to calculate Put-Call Parity?

The Put-Call Parity is an important concept in options pricing which shows how the prices of puts, calls, and the underlying asset must be consistent with one another is calculated using Call Option Price = Spot Price of Underlying Asset+Put Option Price-((Strike Price)/((1+(Risk-Free Rate of Return/100))^(No. of Months/12))). To calculate Put-Call Parity, you need Spot Price of Underlying Asset (S_t), Put Option Price (p_t), Strike Price (X_s), Risk-Free Rate of Return (R_f) & No. of Months (n_m). With our tool, you need to enter the respective value for Spot Price of Underlying Asset, Put Option Price, Strike Price, Risk-Free Rate of Return & No. of Months and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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