The correct answer is: A. binomial parity relationship
Binomial parity relationship is a relationship between the price of a European call option and the price of a European put option, the underlying asset price, the strike price, the risk-free interest rate, and the time to expiration.
The binomial parity relationship states that the price of a European call option is equal to the price of a European put option plus the present value of the strike price times the probability of the option expiring in the money.
The binomial parity relationship can be derived using the following steps:
- Consider a portfolio that consists of a long position in a European call option and a short position in a European put option.
- The payoff of this portfolio at expiration is equal to the payoff of the European call option if the underlying asset price is greater than the strike price, and the payoff of the European put option if the underlying asset price is less than the strike price.
- The value of this portfolio at expiration is equal to the payoff of the portfolio at expiration discounted back to the present value using the risk-free interest rate.
- The value of this portfolio at expiration is equal to the price of the European call option plus the present value of the strike price times the probability of the option expiring in the money.
- Therefore, the price of the European call option is equal to the price of the European put option plus the present value of the strike price times the probability of the option expiring in the money.
The binomial parity relationship is a useful tool for hedging and arbitrage. It can be used to hedge against the risk of changes in the price of the underlying asset, and it can be used to create an arbitrage opportunity if the price of the European call option and the price of the European put option are not in line with the binomial parity relationship.
The other options are incorrect because they do not accurately describe the relationship between the price of a European call option and the price of a European put option.
- Option B, put parity relationship, is a relationship between the price of a European put option and the price of the underlying asset, the strike price, the risk-free interest rate, and the time to expiration.
- Option C, put option parity relationship, is a relationship between the price of a put option and the price of the underlying asset, the strike price, the risk-free interest rate, and the time to expiration.
- Option D, put call parity relationship, is a relationship between the price of a European put option and the price of a European call option, the underlying asset price, the strike price, the risk-free interest rate, and the time to expiration.