*The Business Professor*, updated July 31, 2019, last accessed August 3, 2020, https://thebusinessprofessor.com/lesson/lamda-definition/.

Back to: ECONOMICS, FINANCE, & ACCOUNTING

### Lambda Definition

One of the “Greeks” being lambda refers to the ratio of an option’s change in dollar price to a 1% change in the anticipated price volatility (implied volatility), of an underlying asset. Lambda informs investors of how much the price of an option would change for a specific change in the implied volatility, even if the underlying’s actual price remains the same.

The value of lambda is higher the farther away an option’s expiry date is and drops as the expiry date approaches. Just as each individual option has a lambda, an options portfolio also has a net lambda that’s determined by summing up each individual position’s lambda.

In options analysis, terms such as kappa, sigma, and vega are used interchangeably with lambda.

### A Little More on What is Lambda

Lambda changes when either large price movements occur or there is an increase in the volatility of an underlying asset. For instance, if an option’s price moves 10% higher as volatility rises by 5%, then 2.0 would be its lambda value. Lambda is calculated as the division of the price move by the rise in volatility.

Supposing lambda is high, the option value is highly sensitive to little volatility changes. Supposing lambda is low, volatility changes would have little effect on the option. A positive lambda is linked with a long option which means that as volatility increases, the option becomes more valuable. On the other hand, a negative lambda is affiliated with a short option which means that as volatility decreases, the options gains more value.

One of the core options Greeks is the lambda. Other major options Greeks include:

*Gamma* – measures the rate of delta’s change

*Delta* – measures the effect of a change in the price of the underlying asset

*Theta* – measures the effect of a change in the time left for expiration, also termed as time decay.

### Lambda in Action

If ABC’s share of stock trades at exactly $40 in April and a MAY 45 call is selling for $2, then 0.15 is the option’s lambda and 20% is its volatility.

If there was a 1% to 21% increase in the underlying volatility, then theoretically, the price of the option should rise to $2 + (1 × 0.15) = $2.15.

On the other hand, if there was a 3% to 17% decline instead, then the option should drop to $2 – (3 × 0.15) = $1.55.

Implied Volatility

Implied volatility refers to the gyrations or estimated volatility of the price of a security and is mainly utilized when pricing options. Mostly, but not always, implied volatility increases in a bear market, or when investors believe the price of the asset would decline eventually. It usually, but not always, declines in the bull market, or when investors believe that the asset’s price would rise over time. This movement is as a result of the general belief that bearish markets are riskier than bullish ones. Implied volatility is a method used to estimate the future fluctuations of a Security’s worth based on specific predictive factors.

As stated earlier, lambda the theoretical percentage change in price for each any of every percentage move in implied volatility. Implied volatility is calculated with an options pricing model and this determines what the present market prices are estimating the future volatility of an underlying asset to be. However, it’s possible for the implied volatility to deviate from the realized future volatility.