Put-call parity formula explained: C + PV(K) = P + S. The fundamental options pricing relationship with derivation, examples, and arbitrage applications.
Derivatives priced so no riskless profit is possible. If mispriced, arbitrageurs act to restore equilibrium.
A derivative can be replicated by a portfolio of the underlying and risk-free asset. Replication cost = derivative price.
Forward price = Spot × (1+r)<sup>T</sup> + Storage - Convenience yield. For financial assets: F = S(1+r)<sup>T</sup>.
c + PV(X) = p + S. Links call, put, bond, and stock prices. Violation = arbitrage opportunity.
Model stock as up/down moves. Calculate option values at nodes. Discount back using risk-neutral probabilities.
Forward Price (no income)
Where: S = spot, r = risk-free rate, T = time
Forward with Continuous Dividends
Where: q = continuous dividend yield
Put-Call Parity
Where: c = call, p = put, X = strike, S = stock
Risk-Neutral Probability
Where: u = up factor, d = down factor
Binomial Option Value
Where: Discount expected payoff at risk-free rate
Forward Price
No-arbitrage forward (no income)
Forward Payoff (Long)
Gain if spot > forward
Call Payoff
Right to buy at strike X
Put Payoff
Right to sell at strike X
Put-Call Parity
European options only
Risk-Neutral Probability
Binomial model probability
Binomial Option Value
Discounted expected payoff
Use when:
Avoid when:
Spot price = $50, risk-free rate = 4%, 6-month forward price is:
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