Advanced Options Concepts
Before one can explore the application of various options strategies, one must first be able to analyze the degree of risk they impose. The information below examines several advanced concepts which must be understood before specific strategies can be discussed.
Types of Volatility
Traders who buy and sell options must consider the level of volatility. Volatility can be measured in two ways: Historical and implied:
Historical volatility is an annualized annualized calculation based on the daily price settlements of the actual futures contract. It is usually smoothed out over a period of time by a moving average. Historical volatility reflects price distributions observed in the recent past. For example, a trader may analyse prices for a 50 day, 30 day or 10 day period and calculate the annualized standard deviation.
Implied volatility is a measurement of the expected annual fluctuation of the underlying commodity based on the option premium. A high implied volatility projects greater price swings in historical volatility, while a low implied volatility forecasts smaller price swings.
Before one can explore the application of various options strategies, one must first be able to analyze the degree
of risk they impose. The information below examines several advanced concepts which must be understood before specific
strategies can be discussed.
Risk Analysis of Options
Traders need to assess a fair value for the premium to pay for an option bought or the premium to receive for an option sold.
The use of an option pricing model derives the following information based on a June $46.00 call option on crude oil (priced on May 9^{th} which expires on May 17^{th}) with the underlying June futures (expire on May 22^{nd)}) at $46.14:
Theoretical
 Implied





Price
 Volatility
 Delta
 Gamma
 Theta
 Vega

0.98
 0.3366
 0.5351
 0.1728
 0.0571
 0.0271 
Theoretical Value
Theoretical value and premium are related concepts. The theoretical value of an option is determined by inputs such as
time, volatility, interest rates, futures price and strike price. The premium, which is the total price of an
option, is determined by supply and demand in the marketplace. In general, the more liquid an options market, the closer its premium will be to its theoretical value. Deviations from a fair value enable option traders to exploit inefficiencies in the market.
Delta
The delta indicates the rate of change in the options premium in relation to the underlying futures price. Deltas are positive
for bullish positions and negative for bearish positions. When an option is deeply "inthemoney", its premium changes at a
rate that is approximately equal to the underlying futures price change (delta = 1.0). When an option is "atthemoney", its
premium changes at a rate that is approximately one half (delta = .50) of the underlying futures price change. As an option
moves further "outofthemoney", the rate at which its value changes approaches zero (delta = 0.0).
Gamma
The gamma is sometimes thought of as the "curvature" of an options delta. It is the rate at which an option gains or loses "deltas"
as the underlying contract moves up or down. The gamma is shown in deltas per point change in the underlying futures contract.
For example: The June crude oil $46.00 calls have a delta of .5351, and a gamma of .1728 . If crude settled the day with a $1.00 gain, the new delta would be .7049 (.5351 +.1728) . If the crude declined 1.00, the delta would be .3623 (.5351  .1728).
Theta
The theta, sometimes referred to as the time decay factor, is the rate at which an options' premium declines as time passes.
The theta is usually expressed in points per day. A long options position will always have negative theta, while a short
options position will carry a positive theta. When an option nears expiration, the theta increases exponentially.
For example: The premium on a June $46.00 call is .98 per contract, and has a theta of .0571 The following day, assuming other factors are constant, the March $46.00 calls will be worth .9229 ( .98  .0571).
Vega
The vega of an option is expressed in dollars per day. It measures the change of the premium value for each percentage
point change in volatility. The premium of an option will rise as volatility increases. Conversely, its value will
decline as volatility weakens. It should be noted, that the vega of an option is greatest when the most amount of time
remains before expiration.
For example: On May 9^{th}, the premium for a June $46.00 call is .98 per contract (with the underlying June futures at $46.14) and has a vega of .0271. If volatility closes up 1% on a daily basis, the premium will be $1.0071 (.98 + .0271). If volatility closes down 1%, the premium will be .9529 (.98  .0271)