# Examples of Put-Call Parity

by Tim Plaehn

Put-call parity is a mathematical concept relating to the prices of put and call options on stocks. The parity theory states that puts and calls at the same strike price should offer the same opportunity for a return, based on price changes of the underlying stock. Several real world market conditions can skew put and call option prices away from parity.

### Basic Parity Example

Put-call parity states that put options and call options at the same strike price and expiration, when combined with the underlying stock, should provide equivalent returns. A simple example is put and call prices when the stock is at a strike price. Consider a stock with a current share price of \$60. Put and call options with a strike price of \$60 and the same expiration date should be priced the same. For example, a put and call may each be trading at \$3.00 for a \$60 strike price. The strike price is the value at which the underlying shares will be delivered if a put or call option is exercised.

### Equivalent Options Strategies

Parity between put a call options allows traders to obtain the same profit potential with different strategies. For example, covered call writing is a popular income strategy with call options. A trader buys stock and sells call options against the stock. An equivalent strategy is a cash secured put trade. With this strategy, the trader sells the put and deposits enough cash to buy the stock if the put is exercised. At the same strike price, with option parity, these strategies will provide equivalent returns to an investor.

### Parity and Options Math

In mathematical terms, put and call parity only works for European style options. European options can only be exercised on the expiration date. American style options can be exercised at any time up until expiration. The chance of early expiration distorts the calculations when determining parity prices. The concept of put-call parity is used to validate any new mathematical option pricing model. If the model does not come back with parity pricing for puts and calls on the same stock, the model will not give valid results.

### Real World Conditions

In the real world of options trading, puts and calls will be priced close to parity but not at exact parity. Other factors affect options prices, including bid-ask spreads, market makers, bull markets, bear markets and trader sentiment. The slippage in parity for real world options allows a trader to compare equivalent strategies and select the one that provides a slightly higher potential return. The fact that U.S. stock options do trade American-style also prevents true put-call parity.