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Options Arbitrage Strategy Using Put-Call Parity and Mispricing

Ever wanted to make money in the stock market with little to no risk? Sounds too good to be true, right? Well, that’s where options arbitrage comes into the picture. If you’ve heard about put-call parity but never quite wrapped your head around it, don’t worry—you’re not alone.

In this blog, we’re going to break down how smart traders use the principle of put-call parity and spot price mispricings to create risk-free profit opportunities. Sounds exciting? Let’s dive in.

What is Options Arbitrage Anyway?

Let’s start with an analogy. Imagine going to two markets where apples are sold. In Market A, apples cost $1 each. In Market B, you can sell the same apple for $1.20. You’d naturally buy apples from Market A and sell them at Market B to pocket the difference, right?

That’s arbitrage in action. You’re profiting from a price difference in two markets without taking any risk.

In the world of finance, options arbitrage works in a very similar way. Traders look for differences in option pricing that shouldn’t logically exist according to market rules (like the put-call parity formula) and use those inefficiencies to make a profit.

Understanding Put-Call Parity in Simple Terms

Okay, here’s where things get a little technical—but stick with me! Put-call parity is a principle that defines a relationship between:

• Call Option: The right to buy a stock at a certain price by a certain date.
• Put Option: The right to sell a stock at a certain price by a certain date.
• Stock Price: What the stock is currently trading at.
• Strike Price: The agreed-upon price for the options.
• Time and Interest Rates: Since money has a time value, these also play a role.

The formula goes something like this (don’t worry, we’ll simplify it):

Call Price – Put Price = Stock Price – Present Value of Strike Price

Translated: If a call and put have the same strike price and expiry date, their difference in price should match the difference between the stock price and the discounted strike price. If this doesn’t hold, something fishy (read: profitable) is going on.

How to Profit from the Price Mismatch

Here’s where it gets fun. If there’s a mismatch in this equation, it’s an opportunity!

Let’s say Put-Call Parity Doesn’t Hold True:

Scenario: Call is overpriced compared to put.

• You sell the call (since it’s overpriced).
• You buy the put (since it’s underpriced).
• You also buy the underlying stock to hedge your position.

This combo is called a “conversion” strategy. At expiry, no matter where the stock moves, your gains are locked in. Think of it as setting your GPS to “Profit Mode.”

Another Strategy: The Reversal

Let’s say now the put is overpriced. Do the opposite:

• Buy the call
• Sell the put
• Short sell the stock

This is called the “reverse conversion” or “reversal.” It’s like flipping the script to catch the mispricing from another angle.

Why Does Mispricing Happen in First Place?

Ah, the million-dollar question. Here are a few reasons:

• Market inefficiencies—sometimes prices just don’t catch up fast enough.
• Imbalanced demand and supply for certain options.
• Timing delays in updating option prices.
• Lack of arbitrageurs exploiting the price difference quickly enough.

Once traders notice these price gaps, they’ll jump in to close the arbitrage, eventually aligning the prices back to what put-call parity predicts.

Real-World Example: Bring It to Life

Let’s put it into a simple example.

Suppose the stock of XYZ trades at ₹100. A call option with a strike price of ₹100 trades for ₹8, while a corresponding put trades for ₹10. Assume interest is negligible.

According to put-call parity: Call price should be 2 rupees less than Put price (if stock is ₹100 and strike is ₹100).

But in this case:

• Call is ₹8
• Put is ₹10
• Mismatch of ₹2 exists!

So, you do the following:

• Sell the put (overpriced at ₹10)
• Buy the call (₹8)
• Short the stock (₹100)

At expiry, your profit is locked in—no matter what direction the stock takes. That’s how mispricing opportunities can be turned into cash.

Are There Any Risks?

Honestly, no trade is completely risk-free. Here’s what could go wrong:

• Execution delays: Market prices move fast. You might miss the window.
• Slippage and brokerage costs: Small profits can be wiped out by fees.
• Margin requirements: You may need enough funds to carry out these trades, especially when dealing with short selling or futures.

So yes, it’s a no-risk theoretical strategy—but in practice, you still need to be smart and careful.

When Should You Use This Strategy?

If you’re someone who:

• Loves numbers
• Enjoys low-risk strategies
• Hates market unpredictability

…then options arbitrage using put-call parity could be a sweet spot for your trading journey.

Wrapping It Up

Options arbitrage is like the treasure hunt of the stock market. When market conditions break the golden rule of put-call parity, you have a golden chance too—one where you can earn without betting on market direction.

But remember: opportunities like these vanish quickly. It takes a sharp eye, fast fingers, and a solid understanding of how options pricing works.

Hopefully, this blog helped you get a clearer picture of how to earn from options arbitrage with tools like put-call parity and spotting mispricing. Ready to go hunting for arbitrage gems?

Disclaimer: This blog is intended for educational purposes only. Trading and investing in financial markets involves risk and is not suitable for everyone. Always do your own research or consult with a certified financial advisor before making investment decisions.

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