Final answer:
Put-call parity establishes that the price of a call option and the present discounted value of the underlying stock should equal the price of a put option and the present discounted value of the strike price bond. This equilibrium is maintained by arbitrage opportunities ensuring market efficiency by adjusting the prices of the call, put, stock, and bond to prevent risk-free profit.
Step-by-step explanation:
The concept of put-call parity is fundamental in the pricing of options. It establishes a relationship between the prices of call options and put options of the same underlying asset with the same strike price and expiration date. The principle of put-call parity holds that the price of a call option (when added to the present discounted value of the strike price) should equal the price of a put option (when added to the present discounted value of the underlying asset). Put another way, the cost to buy an asset (via a call option) and the cost to ensure the ability to sell it (via a put option) should be in equilibrium if the market is efficient.
The reason for this parity comes down to arbitrage opportunities. If, for example, calls are undervalued relative to puts, investors can profit by buying calls, selling puts, and hedging with the associated stock and bonds till the options' expiration, exploiting the price discrepancy. Similarly, if the call is overpriced, the reverse strategy would apply, leading to arbitrage until the prices come into balance. These transactions involve the use of the present discounted value concept where potential capital gains, expected dividends, and prevailing interest rates are all taken into account to determine what one should be willing to pay in the present for the future benefits that these financial instruments represent.
Thus, the equivalence between call and stock prices and put and bond prices under put-call parity is not just a theoretical construct; it is a reflection of the forces of supply and demand, arbitrage, and market efficiency in balancing the prices of these financial instruments.