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# Understanding Put and Call Parity and How They Work

6 Mins 26 Aug 2021 0 COMMENT

## Introduction

Options contracts are Derivatives where the buyer has the right to purchase or sell an underlying asset but is not legally obligated to do so. Put and Call parity is the mathematical principle determining the relationship between the Price of Put Options and Call Options. Put and Call parity first appeared in the Middle Ages and was referred to in the following ages by various scholars such as Nelson in 1904, Vincenz Bronzin in 1908, Henry Deutsch in 1910. These scholars’ works have only recently been rediscovered. The first modern introduction to Put and Call parity was by the economist Hans R. Stoll in his paper, “The Relationship Between Put and Call Option Prices,” published in The Journal of Finance in 1969.

## Put and Call parity

The Put and Call parity determines the relationship between Put Options and Call Options of the same category, i.e., those Put and Call Options with the same underlying assets and whose expiration dates and Strike Prices are identical. The Put and Call parity applies only to European-style Options, which can only be exercised on the date of expiration. Put and Call Options to help determine the arbitrage opportunities from the entirety of the Options contract.

## The working of Put and Call parity

The Put and Call parity assumes that the value of the Put Options and the value of the Call Options with the same underlying assets cancel each other out, thereby achieving a zero-value parity for the investors. The Put and Call parity is expressed by the equation C + PV(x) = P + S where:

C = Price of Call Options

PV(x) = Present value of Strike Price (x)

P = Price of Put Option

S = Spot Price, i.e., the present value of the underlying asset.

This basis equation is modified to find the value of more complex variations of the Put and Call parity.

## Meaning of Put and Call Parity

Put and Call parity means that both Put Options and Call Options with the same underlying asset can be used for the same goal in a portfolio. It also means that the implied volatility of an underlying asset is the same for both Put Options and Call Options.

## Importance of the Put and Call parity

Put and Call parity is helpful for investors who want to protect themselves from price fluctuations in the markets since it allows for the calculation of investment required to offset Put and Call Options. That is also useful for speculators since the same equation allows for the analysis of arbitrage opportunities. The Put and Call parity is also important in the valuation of Options and understanding how market forces affect the pricing of Options. It also helps in understanding the relationship between Options pricing and the Price of the underlying assets.

### Conclusion

The Put and Call parity remains an integral part of any attempt at an overall understanding of the pricing of Options and related strategies. Its simplicity is both an advantage as well as a disadvantage. While it allows for the knowledge of the basic Options contracts and their pricing, it can underperform when dealing with complex variations of Options. Such complex variations are better analysed through models, such as the Black-Scholes method and the Monte Carlo method.

Disclaimer

ICICI Securities Ltd. ( I-Sec). Registered office of I-Sec is at ICICI Securities Ltd. - ICICI Centre, H. T. Parekh Marg, Churchgate, Mumbai - 400020, India, Tel No : 022 - 2288 2460, 022 - 2288 2470. The contents herein above shall not be considered as an invitation or persuasion to trade or invest.  I-Sec and affiliates accept no liabilities for any loss or damage of any kind arising out of any actions taken in reliance thereon. The contents herein above are solely for informational purpose and may not be used or considered as an offer document or solicitation of offer to buy or sell or subscribe for securities or other financial instruments or any other product. Investments in securities market are subject to market risks, read all the related documents carefully before investing. The contents herein mentioned are solely for informational and educational purpose.