What is Put-Call parity?
PUT-CALL PARITY refers to the investment sentence at the price of an option to identify a fair price for the PUT or call. According to this sentence, there is a relationship between calls and put, which ensures that there is no arbitration opportunity. If Put-Call's parity holds, no merchant can achieve risk-free profit by simply using the price differences between PUT and call options. The possibility of calling the owner gives the owner the right, but does not require it to buy it a certain amount of the underlying asset at a certain price of exercise in a certain time frame. PUT provides correct but no requirements, sell a specific amount of underlying asset for a certain performance within a certain time frame. The underlying asset may apply to stocks or items such as gold, oil and agricultural products. In this case, cash represented the current value of the exercise price.
parity Put-Call claims that POrtfolio consisting of calls and cash is the same value as the portfolio consisting of the PUT option and the underlying asset. Therefore, the trader would not receive any profit from the risk transaction of the purchase of one portfolio and the sale of the other portfolio. If prices are out of balance, traders would come to make profitable, risk -free transactions until the parity of calls has been restored.
In mathematical terms, PUT-CALL parity can be represented by the formula C + x/(1 + R)
For example, if a trader knows the price of a three -month call option with an exercise price of $ 30 (USD) is $ 3 and the backing asset is awarded for $ 31 when the risk -free rate10 percent, it can find a real price corresponding to the Put option. The formula would be 3 + 30/(1 + 0.1)
0.25 = 31 + P. The calculating P from the formula discovers that the fair price of a three -month option with an exercise price of $ 30 is $ 1.29. If the actual price of the PUT is above or below this value, the trader can benefit from the purchase of the underestimated portfolio and the sale of an overpriced portfolio.
Put-Call parity sentence needs several conditions to work. The possibility of calling and the PUT option must have the same price of exercise, the same underlying asset and the same expiration date. The possibilities must be European options that only allow the owner to be maturity and not earlier. The sentence also assumes that the interest rate is constant. Although deviations from Put-Call parity exist in real life, studies show that the presence of bidding/queries and commissions neutralizes arbitration gains.