Synthetic Stock Strategies

Ultimately, when we roll up our sleeves and get down to the nitty-gritty,options trading is less about having another alternative for trading the direction of the underlying than it is about trading the greeks. Different strategies allow traders to exploit different facets of option pricing. Some strategies allow traders to trade volatility. Some focus mainly on theta.

Many of the strategies discussed in this section present ways for a trader to distill risk down mostly to interest rate exposure.Conversions and Reversals When calls and puts are combined to create synthetic stock, the main differences are the interest rate and dividends. This is important because the risks associated with interest and dividends can be isolated, and ultimately traded, when synthetic stock is combined with the underlying.

There are two ways to combine synthetic stock with its underlying security: a conversion and a reversal.Conversion A conversion is a three-legged position in which a trader is long stock, short a call, and long a put. The options share the same month and strike price. By most metrics, this is a very flat position. A trader with a conversion is long the stock and, at the same time, synthetically short the same stock.

Consider this from the perspective of delta. In a conversion, the trader is long 1.00 deltas (the long stock) and short very close to 1.00 deltas (the synthetic shortstock). Conversions have net flat deltas.The short call contributes a negative delta to the position, in this case, 20.63. The long put also contributes a negative delta, 20.37. The combined delta of the synthetic stock is 21.00 in this example, which is like being short 100 shares of stock.

When the third leg of the spread is added,124 The Basics of Option Greeks the long 100 shares, it counterbalances the synthetic. The total delta for the conversion is zero.Most of the conversion’s other greeks are pretty flat as well. Gamma,theta, and vega are similar for the call and the put in the conversion, because they have the same expiration month and strike price.

Because the trader is selling one option and buying another—a call and a put, respectively—with the same month and strike, the greeks come very close to offsetting each other. For all intents and purposes, the trader is out of the primary risks of the position as measured by greeks when a position is converted. Let’s look at a more detailed example.

A trader executes the following trade (for the purposes of this example,we assume the stock pays no dividend and the trade is executed at fair value):Sell one 71-day 50 call at 3.50,Buy one 71-day 50 put at 1.50, Buy 100 shares at $51.54.The trader buys the stock at $51.54 and synthetically sells the stock at $52. The synthetic price is computed as 23.50 1 1.50 2 50.

Therefore,  the stock is sold synthetically at $0.46 over the actual stock price. Exhibit 6.8 shows the analytics for the conversion. This position has very subtle sensitivity to the greeks. The net delta for the spread has a very slightly negative bias. The bias is so small it is negligible to most traders, except professionals trading very large positions.

Why does this negative delta bias exist? Mathematically, the synthetic’s delta can be higher with American options than with their European counterparts because of the possibility of early exercise of the put. This anomaly becomes more tangible when we consider the unique directional risk associated with this trade.In this example, the stock is synthetically sold at $0.46 over the price at which the stock is bought.

If the stock declines significantly in value before expiration, the put will, at some point, trade at parity while the call loses all its time value. In this scenario, the value of the synthetic stock will be short at effectively the same price as the actual stock price. For example, if the stock declines to $35 per share then the numbers are as follows:With American options, a put this far in-the-money with less than 71 days until expiry will be all intrinsic value.

Interest, in this case, will not factor into the put’s value, because the put can be exercised. By exercising the put, both the long stock leg and the long put leg can be closed for even money, leaving only the theoretically worthless call. The stock-synthetic spread is sold at 0.46 and essentially bought at zero when the put is exercised.

If the put is exercised before expiration, the profit potential is 0.46 minus the interest calculated between the trade date and the day the put is exercised. If, however, the conversion is held until expiration, the $0.46 is negated by the $0.486 of interest incurred from holding long stock over the entire 71-day period, hence the trader’s desire to see the stock decline before expiration, and thus the negative bias toward delta.