Why Mispricing Happens

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Mispricing exploitation in options refers to taking advantage of price inefficiencies between options and their theoretical values. Traders who spot these mismatches can execute strategies to lock in low-risk or risk-free profits—a technique commonly used in arbitrage or relative value trading.

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🧠 Why Mispricing Happens

Cause	Explanation
Volatility misestimation	Implied volatility deviates from actual (realized) vol
Bid-ask spread inefficiencies	Widened due to low liquidity or fast markets
Latency / Delay	Quote or pricing delay between exchanges
Model vs Market Price Gaps	Differences between theoretical model price vs live quote

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📊 Simple Example – Call-Put Parity Violation

Under put-call parity, this must be true (for European options on non-dividend stocks):

$$\text{Call Price} - \text{Put Price} = \text{Stock Price} - \text{Strike Price} \times e^{-rt}$$

If the actual prices violate this equation, an arbitrage opportunity may exist.

Example:

• Stock Price (S) = $100

• Strike Price (K) = $100

• Time to expiration = 1 year

• Risk-free rate = 5%

• Call Price = $10

• Put Price = $14

$$\text{Theoretical difference} = 100 - 100 × e^{-0.05×1} ≈ 4.88$$ $$\text{Actual difference} = 10 - 14 = -4$$

There's a mispricing of nearly $8.88, which creates arbitrage potential.

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🛠 Exploiting This

1. Buy the underpriced option (Call)

2. Sell the overpriced option (Put)

3. Short the stock or hedge exposure as needed

4. At expiry, the mispricing converges, locking in a theoretical profit

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💹 Real-World Strategy: Box Spread Arbitrage

A box spread uses mispricing between vertical call and put spreads.

• Buy a bull call spread

• Sell a bear put spread

• Both with same strikes

• If total cost ≠ width of spread, you can create a riskless gain or synthetic loan

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🚫 Risks in Practice

Risk	Explanation
Execution Risk	Prices can change before all legs are filled
Transaction Fees	Multiple contracts increase cost
Early Exercise Risk	Especially in American options
Model Error	Your calculation of "fair value" could be off

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🧠 Summary

Mispricing exploitation in options is about identifying discrepancies between actual and fair value and building strategies (like box spreads or parity trades) to profit from them. It's a low-risk, high-skill technique often used by quant firms, market makers, or professionals.