Putting Time on Your Side: In Option Trading You Can Position Yourself to Profit with Time as Your Ally. Knowledge of the Effects of Time on Option Prices Can Greatly Enhance Your Chance of Success
Cretien, Paul D., Modern Trader
Time is both an advantage and a problem in option trading. Time to expiration acts like gravity--continuously tugging option values toward final price premiums of zero. Those who buy and sell options try to take advantage of temporary differences between market prices and values that are determined by theoretical or market-based time-related pricing models.
For the past three decades, exchange-traded options in the United States have been priced primarily by theoretical calculations, typically based on the Black-Scholes pricing model. One of the key assumptions in these pricing models is that market price variations are related to the square root of time.
The decline of option prices and time premiums through a 360-day period is shown in "Loss in time premium" (right). The chart of declining value as a function of the square root of time and option premiums falling through time to expiration as computed by the Black-Scholes model shows why option premiums face a continuous downward force as time to expiration gets closer. First, prices vary in relation to the square root of time. Second, options in the U.S. markets are valued mainly by Black-Scholes models that are based on declining values corresponding to the square root of time.
The price curves shown on "Loss in time premium" show the acceleration in decline of value with the shrinking of time to expiration. In their book, The Complete Guide to Option Selling (McGraw-Hill, 2004), James Cordier and Michael Gross recommend selling options that have slightly more than 90 days to expiration. They term this 90-day area the "sweet spot" for option sellers.
Counting back nine bars from the right side of either time premium chart indicates that this area is near the beginning of a more rapid decline in premium as the option's expiration date approaches. At 90 days or more, the market may permit a profitable premium to the seller and still yield an advantage due to the effect of time.
THE TIME FACTOR
Actual market prices vary as to how well they relate to the square root of time and to theoretical pricing by Black-Scholes. In "Time Effect" (right) Black-Scholes prices are computed for Eurodollar calls on Sept. 12, 2006.
By use of a constant standard deviation, futures price and strike price, the only variable is time. In this sample, theoretical prices are closer to market prices for longer times to expiration. Eurodollar option prices are listed as interest rates. Unusually low rates for short-term options are related to temporary rate and price differences caused by Federal Reserve policy actions during 2006.
A device that may be used to find overvalued and undervalued options is the LLP pricing model. Calculations for put and call options on a single underlying asset at one point in time are shown in "How to price Eurodollar options," July 2006. Excel download files for LLP calculations are available at www.futuresmag.com.
The LLP model generates a price curve that includes a number of different strike prices. Option market prices are primarily established by computer models that produce thousands of theoretical prices in a continuous process, and market prices for the most part lie along parabolic curves that are similar to those calculated by the LLP log-log parabola pricing model.
The euro September 2006 call data from Aug. 28, 2006 provided the data for "Euro FX calls" (page 40). Using 10 of 37 strike prices for which option prices were listed by the Chicago Mercantile Exchange (CME) on Aug. 28, the LLP model was used to compute the option price curve.
As shown by "Euro FX calls," predicted prices are close to actual market prices. The option pricing equations generated by the LLP model permit forecasting future prices, given changes in the underlying asset. An LLP price curve may be used for a number of days to provide information for hedging and trading options having a single expiration date. …