Put Call Parity

The put-call parity is an important concept in the domain of financial mathematics. The term is used to explain the connection of the value of a put option and the value of a call option. However, both the put option and call option should have the same date of expiry and strike price.

Deriving the Put-Call Parity
In order to deduce the relation between a put option and a call option it is taken for granted that the options have not been used before the date of their expiry. This presupposition is specifically applicable for the European options.

It may be noted that the derivation of the put-call parity can be done without depending on any specific model.

Equational Representation of Deduction of Put-Call Parity

The following is a numerical representation of the derivation of put-call parity:
C(t) + K . B(t,T) = P(t) + S(t)

  • In this formula:

    C(t) represents the worth of the call option at the time period t
    K represents the strike price
    P(t) represents the worth of the put option
    B(t,T) represents the worth of the bond, which is supposed to mature at the time period T. The dividend paying stocks should be let in B(t,T). The primary reason behind this inclusion is that by nature the prices of options are never adjusted for normal dividends
    S(t) represents the worth of the particular share

However, provided the rate of interest of bond, which is denoted by r, is fixed, the worth of the bond would be represented through the following equational representation:
B(t,T) = e-r(T-t)

Implications of Put-Call Parity
The term put-call parity could mean the equality in value of the put options and call options. It could also mean the parity of unpredictability, which is already implied.

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Last Updated on : 1st July 2013

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