# Option sensitivity

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Minor Greeks What Are the Greeks? These variables are called Greeks because they are typically associated with Greek symbols. Each risk variable is a result of an imperfect assumption or relationship of the option with another underlying variable.

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Key Takeaways The 'Greeks' refer to the various dimensions of risk that an options position entails. The most common Greeks include the Delta, Gamma, Theta, and Vega - which are first partial derivatives of the options pricing model.

The primary Greeks Delta, Vega, Theta, Gamma, and Rho are calculated each as a first partial derivative of the options pricing model for instance, the Black-Scholes model. The number or value associated with a Greek changes over time. Therefore, sophisticated options traders may calculate these values daily to assess any changes which may affect their positions or outlook, or to check if their portfolio needs to be rebalanced.

Below are several of the main Greeks traders look at. For example, assume an investor is long a call option with a delta of 0. For options traders, option sensitivity also represents the hedge ratio for creating a delta-neutral position.

- Practical use[ edit ] For a vanilla option, delta will be a number between 0.
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For example if you purchase a standard American call option with a 0. Net delta for a portfolio of options can also be used to obtain the portfolio's hedge ration. A less common usage of an option's delta is it's current probability that it will expire in-the-money. For instance, a 0.

For example, assume an investor is long an option with a theta of The option's price would decrease by 50 cents every day that passes, all else being equal. Theta increases when options are at-the-money, and decreases when options are in- and out-of-the money.

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Options closer to expiration also have accelerating time decay. Long calls and long puts will usually have negative Theta; short calls and short puts will have positive Theta. By comparison, an instrument whose value is not eroded by time, such as a stock, would have zero Theta.

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This is called second-order second-derivative price sensitivity. For example, assume an investor is long one call option on hypothetical stock XYZ. The call option has a delta option sensitivity 0. 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 is higher for options that are at-the-money option sensitivity lower for options that are in- and out-of-the-money, and accelerates in magnitude as expiration approaches. Gamma values are generally smaller option sensitivity further away from the date of expiration; options with longer expirations are less sensitive to delta changes.

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As expiration approaches, gamma values are typically larger, as price changes have more impact on gamma. Options traders may opt to not only hedge delta but also gamma in option sensitivity to be delta-gamma neutralmeaning that as the underlying price moves, the delta will remain close to zero.

Vega Vega v represents the rate of change between an option's value and the underlying asset's implied volatility. This is the option's sensitivity to volatility.

For example, an option with a Vega of 0.

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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. Conversely, a decrease in volatility will negatively affect the value of the option.

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Vega is at its maximum for at-the-money options that have longer times until expiration. Greek-language nerds will point out that there is no actual Greek letter named vega.

## Using the "Greeks" to Understand Options

This measures sensitivity to the interest rate. For example, assume a call option has a rho of 0.

The opposite is true for put options. Rho is greatest for at-the-money options with long times until expiration.

Minor Greeks Some other Greeks, with aren't discussed as often, are lambdaepsilon, vommavera, speed, zommacolor, ultima. These Greeks are second- or third-derivatives of the pricing model and affect things such as the change in delta with a change in volatility and so on.

They are option sensitivity used in options trading strategies as computer software can quickly compute and account for these complex and sometimes esoteric risk factors.

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