Options Pricing: The Greeks
Many option traders rely on the "Greeks" to evaluate option positions. The Greeks are a collection of statistical values that measure the risk involved in an options contract in relation to certain underlying variables. Popular Greeks include Delta, Vega, Gamma and Theta.
Δ Delta  Sensitivity to Underlying's Price
Delta, the most popular options Greek, measures an option's price sensitivity relative to changes in the price of the underlying, and is the number of points that an option's price is expected to move for each one point change in the underlying. Delta is important because it provides an indication of how the option's value will change with respect to price fluctuations in the underlying instrument, assuming all other variables remain the same.
Delta is typically shown as a numerical value between 0.0 and 1.0 for call options and 0.0 and 1.0 for put options. In other words, option delta will always be positive for calls and negative for puts. It should be noted that delta values can also be represented as whole numbers between 0.0 and 100 for call options and 0.0 to 100 for put options, rather than using decimals. Call options that are outofthemoney will have delta values approaching 0.0; inthemoney call options will have delta values that are close to 1.0.
ν Vega  Sensitivity to Underlying's Volatility
Vega measures an option's sensitivity to changes in the volatility of the underlying. Vega represents the amount that an option's price changes in response to a 1% change in volatility of the underlying market. The more time that there is until expiration, the more impact increased volatility will have on the option's price.
Because increased volatility implies that the underlying instrument is more likely to experience extreme values, a rise in volatility will correspondingly increase the value of an option and, conversely, a decrease in volatility will negatively affect the value of the option.
Γ Gamma – Sensitivity to Delta
Gamma measures the sensitivity of delta in response to price changes in the underlying instrument. Gamma indicates how delta will change relative to each one point price change in the underlying. Since delta values change at different rates, gamma is used to measure and analyze delta. Gamma is used to determine how stable an option's delta is; higher gamma values indicate that delta could change dramatically in response to even small movements in the underlying's price.
Gamma increases as options become atthemoney and decrease as options become in and outofthemoney. Gamma values are generally smaller the further away from the date of expiration; options with longer expirations are less sensitive to delta changes. As expiration approaches, gamma values are typically larger as delta changes have more impact.
Θ Theta – Sensitivity to Time Decay
Theta measures the time decay of an option  the theoretical dollar amount that an option loses every day as time passes, assuming the price and volatility of the underlying remain the same. Theta increases when options are atthemoney; theta decreases when options are in and outofthe money. Long calls and long puts will usually have negative theta; short calls and short puts will have positive theta. By comparison, an instrument's whose value is not eroded by time, such as a stock, would have zero theta.
Trading and analysis platforms, as well as online calculators, can provide options traders with current Greek values for any options contract. Figure 12, for example, shows the Delta, Gamma, Theta, Vega and Rho values for both call and put options. These values will change as other variables, such as strike price, change.
Figure 12: The Greeks 

Strike Width
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BjerksundStensland Model
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DeltaGamma Hedging
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