parity
Conversion / Reversal
Arbitrage strategies that exploit put-call parity violations. A conversion locks in profit when options are mispriced relative to the stock.
Formula
Conversion: +Stock, +Put, -Call (same strike) Profit = C - P - (S - K·e⁻ʳᵀ)
Variables
- Conversion
- Long stock + long put + short call
- Reversal
- Short stock + short put + long call (opposite)
- Profit
- Locked-in risk-free profit if parity is violated
Worked Example
Inputs
- S
- $100
- K
- $100
- C (overpriced)
- $5.00
- P
- $3.38
- Fair C
- $4.62
Calculation Steps
- 1
Buy stock at $100, buy $100 put at $3.38, sell $100 call at $5.00 - 2
Net investment = $100 + $3.38 - $5.00 = $98.38 - 3
At expiration: position always worth $100 (call assigned or put exercised) - 4
Profit = $100 - $98.38 = $1.62 risk-free
Result: Risk-free profit = $1.62 (vs $1.24 expected by parity)
Intuition
In practice, conversions/reversals earn tiny fractions of a cent per share and are executed by high-frequency firms in massive volume. They're the mechanism that keeps put-call parity enforced in real markets.