Put-Call Parity

Put-Call Parity

Put-call parity is a fundamental relationship between European call and put prices on the same underlying asset with the same strike and expiry.

The Relationship

$C - P = S - K e^{-rT}$

Rearranging:

• Call from put: $C = P + S - K e^{-rT}$
• Put from call: $P = C - S + K e^{-rT}$

Where:

• C = call price
• P = put price
• S = current stock price
• K = strike price
• r = risk-free rate (continuously compounded)
• T = time to expiry (in years)

Why Does It Hold?

Consider two portfolios:

1. Long call + cash $K e^{-rT}$
2. Long put + long stock

Both have identical payoffs at expiry, so they must have the same price today (no arbitrage).

Example

Given: S = 100, K = 95, r = 5%, T = 1 year, P = 5.00

$C = 5 + 100 - 95 \cdot e^{-0.05} = 14.6332$

Implement both conversion functions using Python's math.exp.