parity
Synthetic Long / Short
Replicate a stock position using only options. Useful when you can't or don't want to trade the stock directly (margin efficiency, short-sale restrictions).
Formula
Synthetic Long = +Call - Put (same strike & expiry) Synthetic Short = -Call + Put (same strike & expiry)
Variables
- +Call
- Buy a call at strike K
- -Put
- Sell a put at strike K
- K
- Strike price (usually ATM)
- Cost
- Net debit/credit = C - P ≈ S - K·e⁻ʳᵀ
Worked Example
Inputs
- S
- $100
- K
- $100
- C
- $4.62
- P
- $3.38
Calculation Steps
- 1
Buy $100 call = -$4.62 - 2
Sell $100 put = +$3.38 - 3
Net cost = $4.62 - $3.38 = $1.24 debit - 4
Position acts exactly like owning stock for $101.24
Result: Synthetic long for $1.24 debit — equivalent to stock at $101.24
Intuition
Synthetics use less capital than buying stock outright. A $100 stock requires $100 (or $50 on margin). A synthetic might only need $1-2 net plus margin on the short put. Institutions use synthetics to get leveraged directional exposure.