Put-Call-Forward Parity for European Options

Put-Call-Forward Parity for European Options is discussed in this article. You will find it informative and helpful for your research.

Put-call parity

Put call forward parity for European options example

The concept of put-call parity was first used in the publication ‘The Relationship Between Put and Call Option Prices’ written by a public finance economist named Hans R. Stoll in one of his papers which was announced in The Journal of Finance in December 1969 edition.

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The term “put-call” parity concerns a rule that describes the connection among the worth of European put and call options of a similar class. In other words, the concept highpoints the reliabilities of these similar divisions.

Put and call options should have similar fundamental asset or possession, strike price, and date of expiration in order to be classified as having similar classified features.

The put-call parity does not signify the rules but also relates to the European options and can be controlled by a set equation.

Understanding the concept of Put-Call Parity for European Options

Put-call parity advocates that instantaneously holding a small European put and long European call of the similar division will also release the similar return as holding one advancing agreement on the identical underlying asset, with the identical expiration, and a presumptuous value equivalent to the selection’s hit price.

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Assuming the prices of the put and call options differ such that this similar assumption is no longer applicable, an arbitrage chance occurs.

This indicates that complicated dealers can supposedly make an unrestricted risk income. This chance is mostly infrequent and short excited in liquid markets.

The equation that defines put-call parity is:

C + PV(x) = P + S


C represents the value of the European call option

PV(x) represents the present value of the hit price (x),

Which can be deterred from the value on the date of expiration at the risk-free rate

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P represents the value of the European put

S represents spot value or the current market value of the fundament asset

Put-Call Parity and Arbitrage using the formula;

C + PV(x) = P + S

Assuming a firm lacks transaction fees and assumes that TCKR does not keep account of its paid dividend. TCKR options expire in one year with a strike price of $35 we have: Assuming there is an unrestricted risk rate of about 4% and that TCKR stock trades at $25.

C + (35 ÷ 1.04) = P + 25

C + 33.65 = P + 25

33.65 – 25 = P – C

P – C = 8. 65

As earlier stated, Put-call parity allows the analyst to compute the estimated value of a put or a call relative to its other constitutes.

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When the put-call parity is disrupted, it signifies that the value of the put and call select deviates so that this relationship does not hold any longer, then there is an existence of an arbitrage opportunity.

There is a certain vital consideration in the concept Put-Call Parity. Such consideration explains that when one side of the put-call parity equation is simultaneously better than the other, this is an indication that for an arbitrage opportunity.

The trader will be required to offer to sell the extra costly side of the equation and also purchase the cheaper or inexpensive side to create, for all aims and purposes, an unrestricted risk profit.

This shows that after selling a put, shorting the stock, purchasing a call, and purchasing the unrestricted risk asset, it is anticipated that the chance for arbitrage is short-sided and incomprehensible to obtain.

In addition to this intention, the margins can propose a thin such as a massive quality of wealth is needed to take the lead in the situation.


Put-call parity simplify demonstrates the connection that has to be concerning European put and call selection that possesses the identical original asset, expiration, and worth of the hit.

This concept shows the value of a call selection suggests a particular fair value for the consistent put option with a similar hit price and expiration and vice versa.

Put-call parity is not applicable to American selection due to the fact that the dealer can implement it before the date of expiration.

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Assuming, the put-call parity is disrupted, then the chances for arbitrage arise. Thus, the dealer can verify the put-call party by using the formula C + PV(x) = P + S

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