Synthetic Straddles

Straddles are the pet strategy of certain professional traders who specialize in trading volatility. In fact, in the mind of many of these traders, a straddle is all there is. Any single-legged trade can be turned into a straddle synthetically simply by adding stock.Chapter 6 discussed put-call parity and showed that, for all intents and purposes, a put is a call and a call is a put. For the most part, the greeks of the options in the put-call pair are essentially the same. The delta is the only real difference.

And, of course, that can be easily corrected. As a matter of perspective, one can make the case that buying two calls is essentially the same as buying a call and a put, once stock enters into the equation.Take a non-dividend-paying stock trading at $40 a share. With 60 days until expiration, a 25 volatility, and a 4 percent interest rate, the greeks of the 40-strike calls and puts of the straddle are as follows:

Essentially, the same position can be created by buying one leg of the spread synthetically. For example, in addition to buying one 40 call, another 40 call can be purchased along with shorting 100 shares of stock to create a 40 put synthetically.Combined, the long call and the synthetic long put (long call plus short stock) creates a synthetic straddle.

A long synthetic straddle could have similarly been constructed with a long put and a long synthetic call (long put plus long stock). Furthermore, a short synthetic straddle could be created by selling an option with its synthetic pair.Notice the similarities between the greeks of the two positions. The synthetic straddle functions about the same as a conventional straddle.Because the delta and gamma are nearly the same, the up-and-down risk is nearly the same.

Time and volatility likewise affect the two trades about the same. The only real difference is that the synthetic straddle might require a bit more cash up front, because it requires buying or shorting the stock. In practice, straddles will typically be traded in accounts with retail portfolio margining or professional margin requirements (which can be similar to retail portfolio margining). So the cost of the long stock or margin for short stock is comparatively small.

Long Strangle Definition: Buying one call and one put in the same option class, in the same expiration cycle, but with different strike prices. Typical long strangles involve an OTMcall and an OTMput. A strangle in which an ITMcall and an ITM put are purchased is called a long guts strangle.Along strangle is similar to a long straddle inmany ways. They both require buying a call and a put on the same class in the same expirationmonth. They are both buying volatility. There are, however, some functional differences.

These differences stem from the fact that the options have different strike prices.Straddles and Strangles 299Because there is distance between the strike prices, from an at-expiration perspective, the underlying must move more for the trade to show a profit.Exhibit 15.8 illustrates the payout of options as part of a long strangle on a $70 stock. The graph is much like that of Exhibit 15.1, which shows the payout of a long straddle.

But the net cost here is only 1.00, compared with 4.25 for the straddle with the same time and volatility inputs. The cost is lower because this trade consists of OTM options instead of ATM options.The underlying has a bit farther to go by expiration for the trade to have value. If the underlying is above $75 at expiration, the call is ITM and has value. If the underlying is below $65 at expiration, the put is ITM and has value.

If the underlying is between the two strike prices at expiration both options expire and the 1.00 premium is lost.An important difference between a straddle and a strangle is that if a strangle is held until expiration, its break-even points are farther apart than those of a comparable straddle. The 70-strike straddle in Exhibit 15.1 had a lower breakeven of $65.75 and an upper break-even of $74.25.

The comparable strangle in this example has break-even prices of $64 and $76. But what if the strangle is not held until expiration? Then the trade’s greeks must be analyzed. Intuitively, two OTM options (or ITM ones, for that matter) will have lower gamma, theta, and vega than two comparable ATM options. This has a two-handed implication when comparing straddles and strangles.

On the one hand, from a realized volatility perspective, lower gamma means the underlying must move more than it would have to for a straddle to produce the same dollar gain per spread, even intraday. But on the other hand, lower theta means the underlying doesn’t have to move as much to cover decay. A lower nominal profit but a higher percentage profit is generally reaped by strangles as compared with straddles.