The Basics of Put Call Forward Parity
Put-call forward parity states that for European options with the same underlying, strike, and expiration, the call price minus the put price equals the present value of the forward price minus the strike: C − P = e^(−rT) × (F − K), where F is the forward price, K the strike, r the risk-free rate, and T the time to expiration in years. If the prices break this relationship, a trader can combine the call, the put, and a forward to lock in an arbitrage profit, which is why market prices stay close to parity.
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What Is Put Call Forward Parity?
Put-call forward parity is the relationship between European call and put prices expressed with a forward contract instead of the spot price. A long call plus a short put with the same strike and expiration has the same payoff at expiration as a long forward at that strike, so the two must cost the same today: C − P = e^(−rT) × (F − K). The spot version, put-call parity, is C − P = S − K × e^(−rT) for a non-dividend-paying stock.
How Does It Work?
Put-call forward parity depends on the price of the underlying asset, the strike price, the time to expiration, and the cost of carry. The cost of carry is the financing cost of holding the underlying minus any income it pays (such as dividends). It links spot and forward prices: F = S × e^((r − q)T), where q is the dividend yield. Substituting this forward price into the parity equation gives the spot form of put-call parity.
Implications Of Put Call Parity
Put-call parity is mainly an arbitrage and pricing check. If the call is too expensive relative to the put and forward, a trader can sell the call, buy the put, and buy the forward (a conversion) to lock in the difference; if the call is too cheap, the reverse trade applies. Traders also use parity to build synthetic positions: a long call plus a short put behaves like a long forward, and a long stock plus a long put behaves like a long call. A trader who owns the underlying and wants downside protection buys a put, not a call.
Strike Price & Put Call Parity
Strike price refers to the price at which the option buyer can exercise the option and benefit from it. Put call parity can be used to calculate the price of options, which is based on the differences between the spot price of the underlying asset and the strike price.
The strike price moves call and put prices in opposite directions. A higher strike lowers the call price (the buyer pays more to buy the asset) and raises the put price (the buyer can sell the asset for more).
MarketXLS: Analyzing Options and Put Call Parity
MarketXLS is an Excel add-in that pulls option chains and prices into a spreadsheet, for example with =QM_GetOptionChain("AAPL"). To check parity, put the call and put prices for the same strike and expiration side by side, add the stock price (=Last("AAPL")) and a risk-free rate, and compute C − P − (S − K × e^(−rT)). A result far from zero, after allowing for dividends and bid-ask spreads, flags a possible mispricing. Options data is end-of-day on the Standard plan and real-time on the Advanced and Business plans.
