Capital Market Chronicles – Episode 204: UPPER & LOWER BOUNDS OF PUT OPTIONS

 Capital Market Chronicles – Episode 204: UPPER & LOWER BOUNDS OF PUT OPTIONS

(a.k.a. Knowing When Your Put Has Gone Nuts!)

🧩 Introduction

Welcome back, fellow market explorers! If you’ve ever looked at option prices and wondered, “Wait, why is this put so pricey? Did it eat caviar for breakfast?” — you’re not alone. 😅

Today, we dive into the mysterious world of Upper and Lower Bounds for Put Options — those invisible fences that keep option prices from running amok. Think of them as SEBI-approved speed limits for the world of options. 🚦

By the end of this episode, you’ll know exactly when a put option is fairly priced, overpriced, or waving an “Arbitrage Alert!” flag. 🏁

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🎯 Scenario Time!

Let’s meet our hero — ABC Ltd., currently trading at ₹800 per share.
A 1-year European Put Option (remember, these can only be exercised at expiry — no midweek drama!) has a strike price of ₹900.

Now, assuming an 8% risk-free interest rate, the present value (PV) of ₹900 is ₹833.50.

Simple? Perfect. Now, let’s see how this ₹833.50 decides to become the ultimate price police for our put option. 🚨

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💸 The Upper Bound – How High Can You Go?

The Upper Bound for a European Put is determined by the present value of the strike price.
Why? Because no rational trader will pay more for the put than what the strike is worth today.

Example:

• PV of Strike Price: ₹833.50

• Suppose the market price of the Put = ₹860

Hold on! That’s like buying a ₹100 Amazon voucher for ₹105. Who does that? 😲

A clever trader would immediately:
1️⃣ Sell the put for ₹860 💰
2️⃣ Invest ₹833.50 in a risk-free bond (which becomes ₹900 in a year)
3️⃣ Sit back, sip coffee ☕, and enjoy an instant profit of ₹26.50 (₹860 - ₹833.50).

Voilà — arbitrage!
Of course, such profit parties don’t last long. Arbitrageurs pounce, prices adjust, and equilibrium returns.

📏 Moral of the story:
The Upper Bound = PV of the Strike Price.
If prices go higher — cue the market police siren! 🚨

💬 Side Note:
Dividends? Nope — they don’t affect Put upper bounds, since put holders don’t get them. (You can’t cry over a dividend you never owned 🥲).

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🪙 The Lower Bound – The “Basement” Price

The Lower Bound is where our put option refuses to go any lower — because below this, arbitrage steps in again.

Formula fans, rejoice:

Lower Bound = PV (Strike Price) – Current Stock Price

Example:

• Stock Price = ₹70

• Strike Price = ₹75

• PV of Strike Price = ₹73

Therefore, the minimum the put should be worth = ₹3 (₹73 - ₹70).

If it falls below ₹3 — ding ding ding! Another arbitrage alert! 🔔

Here’s what a sharp trader would do:
1️⃣ Buy the cheap put 🏃‍♀️
2️⃣ Borrow ₹73 and buy the stock at ₹70
3️⃣ At expiry, sell the stock at ₹75 (thanks to the put) and repay the borrowed ₹73

That’s a risk-free profit, friends. 💃

📏 Moral of the story:
If the put price is below its lower bound, it’s like spotting ₹500 on the road — smart traders will grab it before it disappears. 😎

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⚖️ Upper & Lower Bounds — Side by Side

For Call Options, the upper bound is simply the current stock price — because no one would sensibly pay more for the right to buy a stock than what it’s actually worth right now.
The lower bound for a call is the stock price minus the present value of the strike price — that’s the least it should ever fall to before arbitrageurs start rubbing their hands in glee. 💼

For Put Options, the upper bound is the present value of the strike price — after all, that’s the most anyone would logically pay for the right to sell at that strike.
The lower bound, on the other hand, is the present value of the strike price minus the current stock price — go below this, and the market’s sharpest traders will jump in to exploit the mispricing faster than you can say “risk-free profit!” 😎

So think of these bounds as a price corridor — the option’s value can move and groove anywhere in between, but it can’t escape the corridor. 🕺

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🧠 Other Fun Factors

⏳ Time Value: As expiry nears, the clock eats into the option’s time value faster than you finish a bag of chips during market hours. 🍟

🌪️ Volatility: Big swings = big premiums. But remember, volatility doesn’t change the theoretical bounds — it just keeps traders guessing!

💰 Interest Rates: A higher rate makes the present value of the strike smaller, nudging both bounds downward.

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🏁 In Summary

The Upper and Lower Bounds of European Put Options act as reality checks — ensuring no one overpays (or undersells) in the options bazaar.

• Upper Bound: PV of Strike Price 🧱

• Lower Bound: PV(Strike Price) – Stock Price 💡

Together, they maintain market sanity and save you from buying an overpriced “bargain.”

So next time someone quotes a put option price that seems too good to be true — check the bounds before you leap! 🚀

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