🔄 Derivatives

Put-Call Parity Formula — Options Pricing Relationship Explained

Q: When is put-call parity violated?

Use when: If c + PV(X) ≠ p + S, arbitrage exists; Buy the cheap side, sell the expensive side. Avoid when: Assuming put-call parity holds for American options (it holds exactly only for European).

Put-call parity formula explained: C + PV(K) = P + S. The fundamental options pricing relationship with derivation, examples, and arbitrage applications.

Key Concepts

No-Arbitrage Pricing

Derivatives priced so no riskless profit is possible. If mispriced, arbitrageurs act to restore equilibrium.

Replication

A derivative can be replicated by a portfolio of the underlying and risk-free asset. Replication cost = derivative price.

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Formulas

From this module

Forward Price (no income)

F₀ = S₀ × (1 + r)^T

Where: S = spot, r = risk-free rate, T = time

Forward with Continuous Dividends

F₀ = S₀ × e^(r-q)T

Where: q = continuous dividend yield

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Master Formula Sheet -- Derivatives

Forward Price

F₀ = S₀ × (1 + r)^T

No-arbitrage forward (no income)

Forward Payoff (Long)

Payoff = S_T - F₀

Gain if spot > forward

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Decision Frameworks

When is put-call parity violated?

Use when:

If c + PV(X) ≠ p + S, arbitrage exists
Buy the cheap side, sell the expensive side

Avoid when:

Assuming put-call parity holds for American options (it holds exactly only for European)

Test Your Understanding

Spot price = $50, risk-free rate = 4%, 6-month forward price is:

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