# Putting put-call parity FOREX

According to the put-call parity concept, there is a fixed link between the time premium of puts and calls that is determined by the options’ volatility and the risk-free interest rate. The idea is intriguing, but retail traders rarely pay much attention to it because its details can seem complex and impractical — relevant only to theory geeks and floor traders who pay miniscule transaction costs. But if you understand the simple equation behind putcall parity, it may change the way you trade certain positions. This formula provides flexibility, because it shows there are two ways to create any options position. For example, if you are bullish on a company, you can either buy its stock or buy a call and sell a put simultaneously (“synthetic stock”), which theoretically offers the same risks and rewards — often with a lower capital requirement. The following four sets of equivalent option positions illustrate how to use put-call parity to find the most practical positions to trade. The put-call parity equation The put-call parity equation states that the value (and therefore the time premium) of puts and calls with the same expiration date and the same strike price is linked. In its simplest form the formula is:
T-bill = Stock – call + put

This means if you purchase a stock and sell a call and buy a put with the same expiration date and strike price, your position will have the same potential risk and return of a Treasury bill. What’s the big deal? Anyone who wants a T-bill should simply buy one instead of trying to clone it by executing three trades and paying three commissions. However, the practical aspects of this formula appear when you rearrange its elements. Table 1 summarizes several position equivalents using put-call parity.

Comparing vertical spreads You can use the original put-call parity equation to find comparable options positions. To find the equivalent to a vertical debit spread, let’s start with a long 85 call: Call85 = + put85 + stock – T-bill
Then, find the alternative to a short 95 call: -Call95 = – put95 – stock + T-bill

Next, combine a long 85 call with a short 95 call to create an 85-95 bull call debit spread: Call85 – call95 = + put85 – put95 + stock – stock + T-bill – T-bill Finally, the answer appears after you simplify the right side of the equation: Call85 – call95 = + put85 – put95 This formula means an 85-95 bull call spread should equal a 95-85 bull put spread. Let’s check this with a trade example. Table 3 shows August option prices for Black & Decker (BDK) when it traded at \$87.76 on June 25. To enter an 85-95 bull call spread, you would buy an 85 call at \$5.70 and sell a 95 call at \$1.05 — an initial net debit of \$4.65. To construct the equivalent 95-85 bull put spread, sell a 95 put at \$7.70 and buy an 85 put at \$2.25 for an initial credit of \$5.45. Table 4 shows both strategies’ potential risk and profit. Figure 2 compares their risk profiles at expiration. Once again, the strategies are equivalent (within \$0.10). In this case it’s more difficult to argue one position has higher transaction costs than the other. However, the put-call parity equation assumes options are European-style, which means option holders can’t exercise them early. This may be true for most index options, but not for equity options.
Exercise and assignment