put call parity
Put Call Parity is the rule that keeps a call option, a put option, the share price and cash all fairly priced against each other, so nobody gets a free lunch.
In plain English
Think of a landlord in Lekki who offers you two separate deals on the same flat. One deal lets you pay a small fee now for the right to rent the flat later at a fixed price. The other lets you pay a small fee now for the right to walk away and hand the flat back later at a fixed price. If those two fees are not set sensibly against each other, and against the flat's current value, a sharp tenant could combine the deals and pocket free money with no risk at all.
That is the whole idea behind put call parity, except the flat is a stock, the two deals are a call option and a put option, and the sharp tenant is really an arbitrageur watching the market like a hawk.
A call option gives you the right to buy a share at a fixed price later. A put option gives you the right to sell a share at a fixed price later. Put call parity says that if you know the price of the call, the current share price, the strike price and the interest rate, you can work out exactly what the put should cost. They are all tied together by one simple equation, and if the market prices break that equation, traders jump in to buy the cheap side and sell the expensive side until balance returns.
Say a Nigerian investor holds shares listed abroad through a UK brokerage app, and notices that a call option and a put option on the same stock, same strike, same expiry, seem priced in a way that does not add up with the share price. That mismatch is a signal, not a coincidence, and it usually closes within minutes as arbitrageurs pounce.
You will not use this formula to price jollof rice or send money to your mother in Enugu, but if you ever trade options, even casually through an international app, this is the calm law that keeps the whole options market honest.
Suppose a share trades at ₦4,000, and a call option with a strike of ₦4,000 expiring in one month costs ₦150. Put call parity tells us the matching put option should cost close to ₦150 too, once you adjust for interest earned on cash over that month. If the put is priced at ₦400 instead, arbitrageurs will sell the expensive put, buy the call, buy a bond, and lock in a profit with no risk, until the price falls back in line.
Questions people ask
Do I need put call parity to trade ordinary shares?
No. It only matters if you trade options, since it links call prices, put prices and the share price together. If you simply buy and hold shares, you can ignore it completely.
Why does interest rate matter in the formula?
Because holding cash instead of shares earns interest over time, and options contracts stretch over weeks or months, so that interest has to be accounted for to keep the pricing fair.
Can ordinary investors profit from put call parity gaps?
In practice these gaps close so fast, often in seconds, that only professional arbitrageurs with fast systems and low costs can reliably capture them.
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