Trading Strategies Profit Making Techniques For Stock_2

Advanced Option Price Movements 57 Typically, professional traders rebalance their positions whenever the UI moves a certain amount, or sometimes they do it every certain number oftimeperiods. Forexample, you maywant torebalance thepositionevery time the underlying moves $1 or at the end of every day, whichever comes first. The usually determining factor on the frequency of rebalancing is the transaction costs versus the rebalancing costs. As a result, floor traders can afford to rebalance more frequently than retail traders. NOT EQUIVALENTS Even though the expression is delta neutral, it is important to realize that no combination of long or short options is the equivalent of or a substitute for a position in the UI (except reversals or conversions; see Chapter 23). All the rebalancing and analysis and arbitrage-based pricing models in the world will not make them equal. If they were equal, there would be no economic need for one of them. Instruments are relatively simple compared to options. With few ex-ceptions, the profit and loss from a UI is strictly related to the price move-ment. An option is subject to many more pressures before expiration, and the profit and loss are nonlinear. The current and future prices of an option are functions of several nonlinear forces. The trader of just UIs is only concerned with the price direction of the UI. An option trader, on the other hand, should take into account price direction, time, volatility, and even dividends and interest rates. As a result, the option strategy may be delta neutral, but the effects of gamma, vega, theta, and even rho may cause profits and losses that are not expected by the delta-neutral trader. The point is to keep monitoring the potential effects of other greeks before and during a trade. C H A P T E R 5 Volatility VOLATILITY AND THE OPTIONS TRADER Volatility is important for the options trader. The expected volatility of the price of the underlying instrument (UI) is a major determinant of the price and value of an option. Some might not consider it important if they are going to hold the po-sition to expiration. They argue that the option will either be in-the-money or it will not. But it is still important for traders to consider volatility be-cause they might be overpaying for the option or miss an opportunity to buy an undervalued option. In addition, by understanding volatility, they might have insights into the potential for the option to expire in-the-money or out-of-the-money. Considering volatility is most important for traders who are not ex-pecting to hold their position to expiration, and it is absolutely critical for traders considering theoretical edge or trading volatility (see Chapter 4 for information on these ideas). One has to know what the implied volatility is before initiating one of these strategies. One has to have an opinion of the future volatility to successfully trade these strategies. It is possible for traders to ignore volatility in their options trading and still be successful, but it is more difficult. Trading options contains more dimensions than trading the UI. Volatility is perhaps the most important additional dimension. 59 60 WHY AND HOW OPTION PRICES MOVE WHAT IS VOLATILITY? Volatility is the width of the distribution of prices around a single point. Usually it is the distribution of past or expected future prices around the current price. Prices go up, and they go down. How far up and how far down is the volatility of those prices. (Remember that volatility is always expressed as an annualized number, even when the volatility is measured over periods greater or lesser than a year; a formula for de-annualizing volatility is given later in this chapter.) Historical or actual volatility is the annualized volatility of UI prices over a particular period in the past. Were prices highly volatile and moved all over the place or were prices stable and moved within a narrow range? Are prices being checked over the past 10 days? Over the past 20 or 100 days? Or over some period in the past? For example, the annualized volatil-ity of the stock market may have been 10 percent over the past 20 days. Expected volatility that is expected by the option trader is the annu-alized volatility of the UI over some period in the future (usually to the expiration of the option). This is a simple projection or expectation. For example, you might think that the volatility of the stock market will be 20 percent over the next six weeks until expiration of the stock index options. Implied volatility is the volatility implied by the current options price. ThiscanbefoundbypluggingthecurrentpriceoftheoptionintotheBlack-Scholes formula (or whatever model is being used) and solving for volatil-ity. Usually, the value for volatility is plugged in and the formula is solved for the value of the option. Here, the situation is reversed—the formula is solved for volatility because the current price is known. BELL CURVES AND STANDARD DEVIATIONS The standard deviation of prices is a description of the distribution of price changes and a good approximation of actual volatility. The mean (commonly called the average) of the prices being examined is basically the middle of the distribution. In the option world, the standard devi-ation is annualized so that various volatilities can be compared on the same scale. Standard deviation is easier to understand with a diagram and a little more explanation. Figure 5.1 shows the closing prices for a particular in-strument, Widgets of America, for the past 60 days. You can see that the prices move around $50 during that period of time. Volatility 61 60 50 40 30 20 10 0 1 3 5 7 9 11131517192123252729313335373941434547495153555759 Days FIGURE 5.1 Daily Prices Standard statistics can be used to calculate the mean and the standard deviation. The standard deviation is simply the statistical description of the variability around the mean. In this case, the mean is $49.47, and the standard deviation is $3.13. This shows that roughly two-thirds of prices will fall within $3.13 of the mean, $49.47. In other words, two-thirds of the time, prices can be expected to range between $46.34 and $52.60. Volatility in the option world is defined as this one standard deviation. A volatility of 20 percent says that the price will vary 20 percent around the mean 68 percent of the time on an annualized basis. The data for examining actual or historical volatility can be precise be-cause they are known. The actual mean and standard deviation can be cal-culated. The data for expected volatility must be assumptions: that the cur-rent price is the mean of the distribution and that prices will be distributed around this mean. It makes sense to assume that prices will be randomly distributed in the future around the current price (the truthfulness of the concept of random price action is discussed later in this chapter). However, the current price of the instrument should not be the actual current price but actually the forward price at expiration of the option. The carrying charges from now until expiration must be taken into account be-cause carrying charges will cause a drift in the current price to the forward price. This is necessary because the forward price is the economic equiva-lentofthecurrentpricecarriedforwardtotheexpirationdate.Theforward price of the instrument is the price that has such carrying costs/benefits as dividends and interest payments built in. Fortunately, carrying charges are built into the Black-Scholes Model. Statistically, the first standard deviation of prices contains roughly 68 percent of all prices, two standard deviations contain nearly 95 percent ... - tailieumienphi.vn