The Theory of Delta-Neutral Trading

Delta-neutral trading involves three steps. First, a trader establishes a delta-neutral position. Second, as the underlying stock price changes and as the net delta of the total position changes away from zero, the trader makes adjusting stock trades according to predetermined rules.Third, the trader closes the entire position, hopefully for a net profit.An adjusting stock trade is the purchase or sale of a specific number of shares of stock that returns the net delta of the total position to zero or approximately zero.

The predetermined rules dictating when stock trades are made can be based on time or stock-price movement. For example, adjusting stock trades based on time might consist of making trades every day at noon or every day shortly before the market closes. Adjusting trades being based on stock-price movement might require making trades whenever the stock price rises or falls $2.00 or when the stock price rises or falls one standard deviation, as explained in Chapter 7. Adjusting stock trades also can be based on the net position delta.

The theory of delta-neutral trading can be illustrated best with two examples, one involving purchased calls and the second involving sold calls. In each example, a trader named Tom will practice delta-neutral trading, which will be explained in five steps. First, Tom will establish a delta-neutral position. The implied volatility of the options that Tom buys or sells will be assumed and identified. Second, Tom will make adjusting stock trades at the close of each trading day.

Closing stock prices for each day are chosen for the sake of the examples, but the deltas and theoretical values of the options that appear in the tables are actual calculations based on those stock prices using the Op-Eval Pro software that accompanies this text. Third, on the fifth day of trading, Tom will close the position. Fourth, Tom will calculate his profit or loss.

Fifth, the conclusion will explain why the example is important, what concepts it illustrates, and what factors in the real world might differ from the example. The reasons that professional market makers and professional speculators might use this strategy will be discussed later in this chapter.Delta-Neutral Trading—Long Volatility Example This first example uses the theoretical values presented in Table 8-6A,the trades presented in Table 8-6B, and the profit-and-loss calculations presented in Table 8-6C. Table 8-6A contains theoretical values and deltas of a 90 Call over five days in the columns and over a range of stock prices in the rows.

The left-most column contains stock prices,and the other columns contain option theoretical values and deltas.In the first column to the right of a stock price of 91.00, for example,“5.71/0.58” appears. The “5.71” is the option’s theoretical value, and the “0.58” is the option’s delta. Six circles appear in Table 8-6A for ease of identification. These circles indicate when trades are made. As noted earlier, the daily price action is created for the sake of the example.In the real world, of course, the market will determine priceaction.

Table 8-6B contains the essential details of all of Tom’s trades in this first example. Column 1 indicates the day of the week. Tom makes two trades on Monday and then one trade on each day from Tuesday through Friday. Column 2 indicates the stock price when a trade is made. Column 3 contains the delta of the 90 Call given the day in column 1 and the stock price in column 2. Note that the deltas in column 3 of Table 8-6B are the same as the deltas in Table 8-6A in the corresponding column (day) and row (stock price).

For example, on Monday, with a stock price of 90.80, the delta of the 90 Call is 0.58 in both tables. Column 4 contains the necessary information about each trade. Column 5 explains briefly the motivation for the trade, and column 6 indicates the ending stock position after the trade is made.Long Volatility—Overview Long volatility means that a position has a positive vega, as defined in Chapter 4.

Long calls and long puts have positive vega. The position in the upcoming exercise is long volatility because the calls are long; that is, they are owned.Before each trade is explained in detail, here is an overview. Tom’s first trade occurs on Monday when he establishes the delta-neutral position.

He subsequently makes adjusting stock trades each day at the end of the day. Finally, he closes the entire position on Friday. There are six trades in Table 8-6B, each of which will be explained next.Transaction costs are not included for the sake of simplicity.Long Volatility Step 1—Opening the Position Tom’s first trade in Table 8-6B creates a delta-neutral position. He establishes the position some time on Monday in a two-part trade.