(09/01/09) Synthetic Put and Call Spreads Made Easy (Part 1)

In order to understand more complex spread strategies involving two or more options, it is essential to understand the arbitrage relationship of the put/call pair. Puts and calls of the same month and strike on the same underlying security have prices that are defined in a mathematical relationship.

They also have distinctly related “Greeks” of vega, gamma, theta, and delta. This article will show how the metrics of these options are interrelated. It will also explore synthetics and the idea that by adding stock to a position, a trader may trade with indifference either a call or a put to the same effect.

Before the creation of the Black-Scholes model, option pricing was hardly an exact science. Traders had only a few mathematical tools available to compare the relative prices of options. One such tool—put-call parity—stems from the fact that puts and calls on the same class, and sharing the same month and strike can have the same functionality when stock is introduced.

Married Put vs. Long Call

For example, traders wanting to own a stock with limited risk can buy a married put, which is a long stock and a long put on a share-for-share basis. The traders have infinite profit potential, and the risk of the position is limited below the strike price of the option. Conceptually, long calls have the same risk/reward profile—unlimited profit potential and limited risk below the strike.

FIGURE 6.1 is an overview of the at-expiration diagrams of a married put and a long call.

Figure 6.1 Long Call vs. Long Stock + Long Put (Married Put)

Click to Enlarge

Married puts and long calls sharing the same month and strike on the same security have at-expiration diagrams with the same shape. They have the same volatility value and should trade around the same implied volatility. Strategically, these two positions provide the same service to a trader, but depending on margin requirements, the married put may require more capital to establish, because the trader must buy not just the option, but also the stock.

The stock component of the married put could be purchased on margin. Buying stock on margin is borrowing capital to finance a stock purchase. This means the trader has to pay interest on these borrowed funds. Even if the stock is purchased without borrowing, there is opportunity cost associated with the cash used to pay for the stock. The capital is tied up. If the trader wants to use funds to buy another asset, he will have to borrow money, which will incur an interest obligation.

Furthermore, if the trader doesn’t invest capital in the stock, the capital will rest in an interest-bearing account. The trader foregoes that interest when he buys a stock. However the trader finances the purchase, there is an interest cost associated with the transaction.

Both of these positions, the long call and the married put, give a trader exposure to stock price advances above the strike price. The important difference between the two trades is the value of the stock below the strike price—the part of the trade that is not at risk in either the long call or the married put. On this portion of the invested capital, the trader pays interest with the married put (whether actually or in the form of opportunity cost). This interest component is a pricing consideration that adds cost to the married put and not the long call.