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Greeks

The Greeks describe an option's sensitivity to changes in different factors. Here we use ordinary stock options, with other pricing inputs held fixed.

Delta

The size of the price change

How much does the option value change when the underlying moves by one unit?

Calls: the same stock-price move changes the option price more far above the strike, and less far below it. Puts: a rising stock price usually lowers the option price; a falling stock price usually raises it.

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For example, with Delta = 0.5 and other factors unchanged:

  • The stock rises by 1 yuan
  • The option price rises by about 0.5 yuan

These are local estimates. Option-price amounts are per share; multiply by the contract multiplier for one contract.

Gamma

Delta's accelerator

For a one-unit rise in the underlying, approximately how much does delta change?

Near the strike and close to expiration, the same stock-price move usually causes a larger change in delta. Far from the strike, the change in delta is usually smaller.

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For example, with Delta = 0.5, Gamma = 0.04 and other factors unchanged:

  • The stock rises by 1 yuan
  • Delta becomes approximately 0.54

These are local estimates. Option-price amounts are per share; multiply by the contract multiplier for one contract.

Theta

The speed of time decay

How does the option value change as one day passes?

Bought options usually lose value as time passes. Near the strike, daily decay typically speeds up as expiration approaches. Far from the strike, the daily loss is often smaller. The daily amount is not fixed.

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For example, with Theta = -0.08 and other factors unchanged:

  • Time passes by 1 day
  • The option price falls by about 0.08 yuan

These are local estimates. Option-price amounts are per share; multiply by the contract multiplier for one contract.

Vega

Sensitivity to expected price swings

How does the option value change when implied volatility rises by one percentage point?

Expecting larger swings usually makes ordinary options more expensive; higher vega means a larger response to the same volatility change. Sensitivity is usually greater with more time remaining, and weaker near expiration.

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For example, with Vega = 0.12 and other factors unchanged:

  • Implied volatility rises 20% → 21%
  • The option price rises by about 0.12 yuan

These are local estimates. Option-price amounts are per share; multiply by the contract multiplier for one contract.

Rho

Interest-rate sensitivity

How does the option value change when the risk-free interest rate used in pricing rises by one percentage point?

When rates rise, calls generally become more expensive and puts cheaper. The effect is usually larger with more time remaining, and smaller near expiration.

View example

For example, with Rho = 0.04 and other factors unchanged:

  • The interest rate rises 4% → 5%
  • The option price rises by about 0.04 yuan

These are local estimates. Option-price amounts are per share; multiply by the contract multiplier for one contract.

For the same option and quantity, a short position has the opposite Greek signs to a long position.

Several factors can change together: a call can lose value even as the stock rises if time decay or falling implied volatility outweighs the gain from the stock move.