Put-Call Parity Calculator

What is Put-Call Parity?

Put-Call Parity is a fundamental principle in options pricing that defines the relationship between the prices of European call and put options with the same strike price and expiration date. It states that a portfolio of a long call and short stock position should equal a portfolio of a long put and long bond position.

The Formula

This can be rearranged to solve for any variable. The formula accounts for the time value of money through the present value of the strike price and adjusts for dividends.

Arbitrage Opportunities

When put-call parity is violated, arbitrage opportunities exist. Traders can exploit these mispricings by simultaneously buying undervalued options and selling overvalued ones, along with appropriate stock and bond positions, to lock in risk-free profits.

• • If C + PV(K) > P + S: Sell call, buy put, buy stock, borrow
• • If C + PV(K) < P + S: Buy call, sell put, short stock, lend

Important Assumptions

• • Applies to European options (cannot be exercised early)
• • No transaction costs or taxes
• • Ability to borrow and lend at the risk-free rate
• • No arbitrage opportunities in the market
• • Continuous dividend yield (if applicable)

Use Cases

• • Verifying options pricing consistency
• • Identifying arbitrage opportunities
• • Calculating implied values of options
• • Risk management and hedging strategies
• • Options market making and trading
• • Academic research and education