parity
Put-Call Parity
The fundamental relationship linking European calls, puts, stock, and bonds. If violated, an arbitrage opportunity exists.
Formula
C - P = S - K · e⁻ʳᵀ
Variables
- C
- Call option price
- P
- Put option price
- S
- Current stock price
- K
- Strike price
- r
- Risk-free interest rate
- T
- Time to expiration (years)
Worked Example
Inputs
- S
- $100
- K
- $100
- r
- 5%
- T
- 0.25
- C
- $4.62
Calculation Steps
- 1
K · e⁻ʳᵀ = 100 × e⁻⁰·⁰¹²⁵ = 98.76 - 2
P = C - S + K · e⁻ʳᵀ - 3
P = 4.62 - 100 + 98.76
Result: P ≈ $3.38 — verified against Black-Scholes put
Intuition
Put-call parity means you can create any one of the four (call, put, stock, bond) by combining the other three. A long call + short put at same strike = synthetic long stock. Market makers use this constantly to check for mispricing.