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# Mastering put call parity: Essential insights for options trading

Put Call Parity is a concept in options trading that showcases the relationship between put and call options and their underlying assets. A put option is a legal contract that gives the right to sell an asset at a predetermined price. A call option is a contract that gives the right to buy at a fixed price.

This principle ensures that put and call options prices match that of their underlying assets.

Once you understand put call parity, you will be better equipped to capitalise on trading and seeking arbitrage opportunities. Let’s discuss what is put call parity and its impacts on the financial world.

## What is put call parity?

Put call parity is a fundamental principle in options pricing that establishes a relationship between the prices of put and call options with the same underlying asset, strike price, and expiration date.

The principle says that the cost of a European call option and a European put option – the two options sell simultaneously at the same strike price and exercise date – ought to be the same after accounting for the present value of the strike price and any dividends or interest that will be received during the life of the options.

In other words, a call option plus a present value of the strike price is equal to the put option plus the current price of the underlying asset. This principle helps in understanding options pricing and identifying arbitrage opportunities in the financial markets.

## What’s the formula for put call parity?

The put call parity arbitrage calculation allows traders to exploit any discrepancies in option pricing, thereby potentially profiting from market inefficiencies. The put call parity formula can be stated as:

C + PV(K) = P + S, Where:

• C: Price of the European call option
• PV(x): Present value of the strike price (K), discounted to the present time using a risk-free interest rate
• P: Price of the European put option
• S: Current price of the underlying asset (e.g., stock)

The formula for put call parity for a non-dividend paying security is c = S + p — Xe–r(T– t), where:

• X: is exercise price of option
• e: is Euler’s constant, approximately 2.71828
• r: is continuously compounded risk free interest rate
• T-t: is term to expiration measured in years

If put call parity is violated, an arbitrage opportunity exists. For example, if portfolio B is calling P + s0, and portfolio A is the call option plus the present value of the strike, then ₹33.25 is not the same as ₹32.26. In this case, an arbitrageur would exploit this arbitrage opportunity by buying the cheaper portfolio and selling the costlier one and booking an arbitrage (risk-free) profit.

## put call parity example

Consider a scenario where a stock in the Indian market, let’s call it XYZ Ltd., is currently trading at ₹1,000 per share.

• Call Option: A call option grants the holder the opportunity to purchase shares of XYZ Ltd. at a predetermined price. Suppose a call option with a strike price of ₹1,050 and an expiration date in 3 months is priced at ₹60.
• Put Option: On the other hand, a put option grants the holder the right to sell XYZ Ltd. shares at the strike price. Let’s say a put option with the same expiration date and the strike price of ₹1,050 is priced at ₹40.

put call parity states that there should be a consistent relationship between the prices of put and call options and the value of the underlying stock.

• Call Option Value: If the call option allows you to buy the stock at ₹1,050, but it’s currently trading at ₹1,000, it’s not beneficial to exercise the option. Hence, the call option value should be Strike Price – Current Stock Price = ₹1,050 – ₹1,000 = ₹50. But it’s trading at ₹60, so there’s a premium of ₹10.
• Put Option Value: Similarly, if the put option allows you to sell the stock at ₹1,050 when it’s trading at ₹1,000, it’s advantageous. Hence, the put option value should be Current Stock Price – Strike Price = ₹1,000 – ₹1,050 = -₹50 (or zero if negative values are not allowed). But it’s trading at ₹40, so there’s a premium of ₹10.

This ₹10 difference in premiums represents a potential arbitrage opportunity, as per the put call parity principle. You could exploit this discrepancy to profit until the prices align with the parity relationship, thereby maintaining market efficiency.

Understanding this concept can be visualized through a put call parity graph, illustrating the relationship between call and put option prices.

## Why is put call parity important?

put call parity is important for several reasons in options trading:

### 1. Arbitrage opportunities

Put call parity helps identify mispriced options, leading to potential arbitrage opportunities. If put and call options with the same strike price and expiration date are not priced according to the parity relationship, traders can exploit the price discrepancies to earn risk-free profits.

### 2. Options pricing

Understanding put call parity is crucial for pricing options accurately. By knowing the relationship between put and call prices, traders can assess whether options are overvalued or undervalued relative to their theoretical values, enabling better decision-making in buying or selling options.

### 3. Risk management

put call parity aids in risk management strategies by providing insights into hedging techniques. Traders can use the parity relationship to construct hedged positions that mitigate risk exposure, thus safeguarding their portfolios against adverse market movements.

### 4. Market efficiency

Put call parity contributes to the efficiency of options markets by ensuring that prices of related options and underlying assets remain in equilibrium. When put call parity holds true, it implies that market prices reflect all available information, leading to more efficient price discovery and reducing opportunities for market inefficiencies.

## Conclusion

Knowing about put call parity is super important for trading options. It helps you determine fair prices, spot good deals, and stay safe from risks. As you keep learning about finance, remember that knowing more is always good. Try using StockGro to learn more about options and become even better at trading.

## FAQs

How does put call parity work?

Put call parity establishes that the price of a call option, the price of a put option, and the underlying asset’s price should be related in a specific way. This relationship helps you assess the relative value of options.

Why is put call parity important?

Put call parity is crucial because it allows you to identify mispriced options and potential arbitrage opportunities. Understanding this concept helps you make more informed decisions in the market.

What factors influence put call parity?

Put call parity is influenced by factors such as interest rates, dividends, and time to expiration. Changes in these variables can affect the relationship between option prices and underlying asset prices.

Can put call parity be violated?

In theory, put call parity should hold true under certain conditions. However, in real-world situations, market inefficiencies or transaction costs may lead to temporary violations of put call parity.

How can I use put call parity in trading?

You can use put call parity to evaluate the fairness of options prices and identify potential trading opportunities. By understanding this concept, you can better analyze market trends and make informed trading decisions.

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