Describe the manner in which PUT-CALL parity can be used to price other types of derivatives securities, such as Futures or Forward contracts
PUT-CALL parity is a relationship between the prices of put options and call options with the same underlying asset, strike price, and expiration date. It states that the combination of a long call option and a short put option, along with holding the underlying asset in the appropriate ratio, must have the same cash flow as a risk-free investment.
To understand how PUT-CALL parity can be used to price other types of derivative securities, like futures or forward contracts, we need to break down the formula for PUT-CALL parity, which is as follows:
C - P = S - X / (1 + r)^T
Where:
C = Price of the call option
P = Price of the put option
S = Spot price of the underlying asset
X = Strike price of the options
r = Risk-free interest rate
T = Time to expiration
Now, let's consider futures and forward contracts. Both of these derivative securities have an underlying asset, a fixed price (known as the futures price or forward price), and an expiration date. Their payoffs at expiration are also similar to the payoffs of options.
To use PUT-CALL parity to price futures or forward contracts, we can make a couple of adjustments to the formula. First, we replace the call and put option prices (C and P) with the difference between the futures (F) or forward price (F) and the underlying spot price (S). Second, we replace the strike price (X) with the futures (F) or forward price (F). The formula then becomes:
(F - S) = (F - X) / (1 + r)^T
This adjusted formula allows us to derive the fair value of the futures or forward contract by comparing the spot price of the underlying asset with its futures or forward price. By rearranging the formula, we can solve for the futures or forward price:
F = [S + X / (1 + r)^T] / 2
Where:
F = Futures or Forward price
This formula helps derive the theoretical price of futures or forward contracts by taking into account the interest rate and the time to expiration.
So, to summarize, PUT-CALL parity can be used as a pricing model for other derivatives, such as futures or forward contracts, by making suitable adjustments to the formula that relate the prices of put and call options.