Trading Exercises Introduced

The four exercises that follow demonstrate three trading techniques that market makers use. First, they trade delta-neutral to avoid the risk of market direction. Second they use implied volatility to set and adjust bid and ask prices. Third, market makers can be indifferent about which options they buy or sell because buying on the bid and selling at the ask can lead to profitable conversions, reverse conversions, butterfly spreads, and box spreads. The following exercises give only a glimpse of the many trades this technique makes possible.

All four trading exercises use the theoretical values, deltas, and vegas in Table 9-7. The stock price range is from 83.60 to 85.00, the volatility assumption is 32 percent, and the days to expiration, interest rates, and dividends are as stated at the bottom of the table.Each exercise has its own assumptions about the width of the bidask spread and about the number of bid-ask price adjustments, if any.

These variations are consistent with the real world in that different options markets have different characteristics, one of which is the width of bid-ask spreads. Such differences might be the result of stockprice volatility, of volume of trading in the underlying stock or in the options themselves, or of a specific company event, such as a pending earnings announcement.Each exercise uses three tables that explain the activities of hypothetical trader, Ross. The first table, labeled “Instructions,” is an overview of the steps of the exercise.

In the first step, Ross makes a market in one or more options, which involves stating bid and ask prices given levels of volatility. In the second step, Ross makes a trade at one of those prices. Subsequently, in the third step, the stock price changes,and Ross establishes new bid and ask prices and makes more trades.The second table contains a step-by-step explanation of how Ross implements the instructions in the first table, and the third table summarizes the exercise.

Profit and loss are calculated by comparing the price at which a position is established to its theoretical value. A conclusion is stated at the end of the third table that summarizes the essential point of the exercise.Exercise 1: Buying Calls Delta-Neutral Table 9-8A presents an overview of the two trades in this example. Ross is instructed first to set bid and ask prices for the 85 Call at stated levels of volatility and second to make an opening delta-neutral trade.

The third instruction is to adjust the bid and ask prices, and the fourth is to close out the whole position.
Steps 1 through 4 in Table 9-8B detail how Ross follows each instruction.In step 1, he sets bid and ask prices for the 85 Call at volatility levels of 32.0 and 33.0 percent, respectively, with the stock price 84.60.Given a theoretical value of 4.28, and assuming 32.0 percent volatility and a vega of 0.10, Ross sets the bid price at 4.28 (32.0 percent) and the ask price at 4.38 (33.0 percent).

Note that the ask price is 0.10 or one vega greater than the bid price.In step 2, Ross buys 10 of the 85 Calls on the bid and sells stock short to hedge the options delta-neutral. Since the 85 Call has a delta of 0.52 with the stock at 84.60, buying 10 of these calls requires that Ross sell 520 shares short.Step 3 reflects how Ross adjusts the bid and ask prices to volatility levels of 31.8 percent bid and 32.8 percent ask.

Given the new stock price of 83.80, a theoretical value of 3.88, and a vega of 0.10,the new market for the 85 Call is 3.86 bid (31.8 percent) and 3.96 ask (32.8 percent). The volatility is adjusted down for two reasons.First, if another sell order comes into the market that Ross might have to buy, then a lower bid price makes it possible for him to scale into a bigger position of 85 Calls at a lower average level of volatility.

Second, the lower volatility hopefully will entice buyers into the market. The specific adjustment of two-tenths of a percent volatility is the result of Ross’s personal judgment. Each trader makes such a decision individually based on knowledge and experience. In step 4, Ross closes the position by selling the 10 calls at the ask price of 3.96 and purchases, or covers, the short shares at 83.80.

Exercise 1 concludes with the profit-and-loss calculations presented in Table 9-8C. The 10 calls Ross purchased at 4.28 each and sold at 3.96 each resulted in a loss of $320 [(4.28  3.96)  $100], not including commissions. The 520 shares he sold short at 84.60 and covered (bought) at 83.80 resulted in a profit of $416 [($84.60  $83.80)
 520], not including commissions. The net result, therefore, was a profit of $96 before costs. As in the exercises in Tables 9-1 and 9-2, the conclusion from this exercise is that buying on the bid, selling at the ask, and trading delta-neutral can earn profits.