🎯 Capital Market Chronicles – Episode 205: UPPER & LOWER BOUNDS OF CALL OPTIONS
(a.k.a. The Ceiling and Floor of Optimism!)
Introduction
Every trader dreams of limitless profits — until the market politely reminds them that even optimism has boundaries! 😄
Understanding the upper and lower bounds of call options isn’t just theory — it’s your map to knowing how high (or low) your call option can realistically go. These invisible guardrails keep option prices fair and stop overenthusiastic traders from floating too far into the clouds.
Scenario
Let’s set the stage:
ABC Ltd’s stock is currently priced at ₹800.
A 1-year European call option has a strike price of ₹700.
The present value of ₹700 discounted at 8% is ₹648.
Now, let’s explore where this call option can — and can’t — wander.
☁️ Upper Bound – The Ceiling of Ambition
Think of this as the market’s way of saying, “You can’t fly higher than the stock itself.” 🚀
The upper bound of a European call option equals the current stock price.
Why?
Because no sane trader would pay more for the right to buy a stock in the future than they would to simply… buy it today!
Example:
If the stock is ₹800, that’s the absolute cap.
If a call option trades at ₹820, it’s basically shouting, “Arbitrage me!” 💸
An alert trader could:
-
Sell the overpriced option for ₹820,
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Buy the stock directly at ₹800,
-
Pocket a clean ₹20 profit — risk-free!
So, anytime the call’s price dares to cross the stock price, the invisible hand of arbitrage smacks it right back into line. 🖐️
💡 Fun Fact:
Dividends can nudge the upper bound slightly lower — after all, call holders don’t get dividend cheques, stockholders do!
📉 Lower Bound – The Safety Net of Sanity
Now, let’s talk about the lower bound — the market’s version of a safety floor. 🧯
This limit is set by the difference between:
👉 the current stock price and
👉 the present value of the strike price.
Example:
Stock = ₹100
Strike = ₹90
PV(Strike) = ₹87
The call option’s lower bound = ₹100 - ₹87 = ₹13.
If the option somehow trades below ₹13, that’s your golden arbitrage ticket! 🎟️
Buy the undervalued call, borrow ₹87, buy the stock, and watch the math do the magic when the option expires. 🧮
Market efficiency quickly steps in to fix such mispricings.
⚖️ The Balance Sheet of Bounds
Let’s summarise our guardrails:
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Call Options:
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Upper Bound → Stock Price
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Lower Bound → Stock Price – PV(Strike Price)
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-
Put Options:
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Upper Bound → PV(Strike Price)
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Lower Bound → PV(Strike Price) – Stock Price
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So basically, every option has its price corridor — it may dance 🕺 within those walls, but never break free!
🔍 Other Influencers
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⏳ Time Value: As expiry nears, the room to dance narrows — premiums shrink.
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🌪️ Volatility: More turbulence means more premium — but still within bounds.
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💰 Interest Rates: Rising rates tweak the PV of strike price, shifting both bounds a bit.
🧠 Summary
The upper and lower bounds of call options keep optimism disciplined and pricing rational.
The upper bound reminds us — you can’t pay more than the stock itself.
The lower bound ensures — you don’t sell yourself short below fair value.
Together, they form the invisible corridor that keeps the world of options logical, balanced, and occasionally, delightfully ironic. 😄
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