What is 'Lambda'

One of the "Greeks," lambda is the ratio of the dollar price change of an option to a 1% change in the expected price volatility, also called the implied volatility, of an underlying asset. Lambda tells investors how much an option's price will change for a given change in the implied volatility, even if the actual price of the underlying stays the same. 

Lambda's value is higher the further away an option's expiration date is and falls as the expiration date approaches. Just as individual options each have a lambda, an options portfolio has a net lambda that is determined by adding up the lambdas of each individual position.

In options analysis, lambda is used interchangeably with the terms vega, kappa, and sigma.


Lambda changes when there are large price movements, or increased volatility​​​​​​​, in the underlying asset. For example, if the price of an option moves higher by 10% as volatility rises 5%, then its lambda value is 2.0. Lambda is calculated by the price move divided by the volatility rise.

If lambda is high, the option value is very sensitive to small changes in volatility. If lambda is low, changes in volatility will not have much of an effect on the option. A positive lambda is associated with a long option and means that the option becomes more valuable as volatility increases. Conversely, a negative lambda is associated with a short option and means the option becomes more valuable as volatility decreases. 

Lambda is one of the most important options Greeks. Other important options Greeks include:

  • Delta, which measures the impact of a change in the underlying asset's price
  • Gamma, which measures the rate of change of delta
  • Theta, which measures the impact of a change in time remaining to expiration, also known as time decay

Lambda in Action

If a share of stock for ABC trades at $40 in April and a MAY 45 call sells for $2. The option's lambda is 0.15 and volatility is 20%.

If the underlying volatility increased by 1% to 21%, then theoretically, the option price should move higher to $2 + (1 x 0.15) = $2.15.

Alternatively, if volatility declined by 3% to 17% instead, then the option should fall to $2 - (3 x 0.15) = $1.55

Implied Volatility

Implied volatility is the estimated volatility, or gyrations, of a security's price and is most commonly used when pricing options. Usually, but not always, implied volatility increases while the market is bearish, or when investors believe the asset's price will decline over time. It usually, but not always, decreases when the market is bullish, or when investors believe that the price will rise over time. This movement is due to the common belief that bearish markets are riskier than bullish markets. Implied volatility is a way of estimating the future fluctuations of a security's worth based on certain predictive factors.

As stated previously, lambda measures the theoretical percentage price change for each percentage move in implied volatility. Implied volatility (IV) is calculated using an options pricing model and determines what the current market prices are estimating an underlying asset's future volatility to be. However, the implied volatility may deviate from the realized future volatility.

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