## Monday, December 3, 2012

### Nations, Options Math for Traders

Scott Nations, probably best known as a contributor to CNBC, is a trader and a financial engineer. Both of these skills are evident in Options Math for Traders: How to Pick the Best Option Strategies for Your Market Outlook (Wiley, 2012). I should say up front, however, that this book is not for the reader in search of lots of formulas. Even the appendix has formulas for only such basic concepts as standard deviation, realized volatility, linear interpolation, and annualizing yield. The text itself has but a single formula—the Black-Scholes pricing model. In brief, it is a book for “the rest of us.”

The primary themes of the book are volatility, skew, time decay, and the bid/ask spread. The strategies analyzed are covered calls and their synthetic equivalent selling puts, calendar spreads, risk reversal, and vertical spreads.

In this post I’m going to focus on a single chapter—vertical spreads—to illustrate how Nations brings the threads of his book together. I’m offering mere snippets out of context. If the excerpts I quote are not intelligible, it’s not the author’s fault (Nations is a clear writer) but the result of my overly aggressive scissors.

Nations uses vertical spreads to get bearish exposure to the underlying. Why bearish? Because skew works against bullish vertical spreads. As examples, he takes a 180/200 put debit spread and a 210/230 call credit spread. “In both the put spread bought and the call spread sold, skew generated a net benefit. There would certainly be other phenomena that would be helping or hurting these trades. The volatility risk premium would be helping the call spread since our trader would likely be selling the 210 strike call for more than it was worth, and that benefit would probably overwhelm the damage that the volatility risk premium would do to the profitability of the 230 strike call option bought. Time decay would also likely help the profitability of the call spread, since the daily erosion received from the call our trader is short (the 210 strike call) is going to be greater than the daily erosion paid on the option our trader is long (the 230 strike call).” (p. 219) By contrast, the profitability of the put spread will likely be hurt by the volatility risk premium and time decay.

How does one determine whether a vertical spread is expensive or cheap? A reasonable way to go about this is to compare the cost of the spread to the width of the spread, taking into consideration how close it is to being at-the-money. If, for instance, a put spread costs \$3.30 and the spread is \$20 wide, the spread would cost 16.5% of the width of the spread. This ratio is “pretty inexpensive given that one strike is so close to at-the-money.” (p. 226)

And how good a hedge is one leg of the spread for the other? “As vertical spreads get wider each option is a less effective hedge for the other option…. As a vertical spread gets wider, the option that is closer to at-the-money starts to act more like an outright option rather than as part of a spread.” (p. 229)

A last take-away: “Skew tends to generate a much smaller benefit for short call spreads than for long put spreads; the difference in implied volatility is lower for call spreads. … The result of selling the strike price that is in the ‘trough’ of the skew curve is that every possible call spread using that strike as the short strike is worse off because of skew.” (p. 232)

If these excerpts whet your appetite, I can heartily recommend Options Math for Traders. No, it doesn’t cover straddles and strangles and wing spreads. But once you understand calls and puts and vertical spreads, you’re a long way toward grasping these other strategies. Moreover, Nations does a very good job with calendars, which I personally consider one of the toughest option spreads to trade well. It’s an “in the trenches” book and as such could be of great help to the intermediate options trader.