Final answer:
The discounted value in the put-call parity formula is the strike price (D). This formula establishes a relationship between the prices of European put and call options to prevent arbitrage opportunities. The present value of the strike price is discounted at the risk-free interest rate over the options' lifespan. The correct option is D. strike price
Step-by-step explanation:
The value that is discounted in the put-call parity formula is the strike price (D). The put-call parity is an important principle in options pricing which shows the relationship between the price of a European put option and a European call option with the same strike price, expiration, and underlying stock. The formula helps ensure that there's no arbitrage opportunity for the prices of put and call options. According to the formula:
C + PV(X) = P + S
where:
- C is the price of the European call option,
- PV(X) is the present value of the strike price (X), discounted at the risk-free interest rate over the life of the options,
- P is the price of the European put option, and
- S is the current price of the stock.
The present value of the strike price is calculated using exponential decay based on the risk-free rate to account for the time value of money, which is a core concept in finance.
This means that when you are projecting forward or backward in time, money has a time value, and the amount needs to be adjusted appropriately by discounting it when looking back from the future or compounding it when projecting into the future. The correct option is D. strike price