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 $2.50. The option's lambda 0.16 and volatility is 20%.

If the underlying volatility increased by 1% to 21%, then theoretically, the option price should move higher to $2.50 + (1 x 0.16) = $2.66.

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.

  1. Vega

    The measurement of an option's sensitivity to changes in the ...
  2. Volatility Arbitrage

    Volatility arbitrage is a trading strategy that attempts to profit ...
  3. Option Premium

    1. The income received by an investor who sells or "writes" an ...
  4. VIX Option

    A VIX option is a derivative security based on the CBOE Volatility ...
  5. Volatility Quote Trading

    A method of quoting option contracts whereby bids and asks are ...
  6. Volatility Swap

    A forward contract whose underlying is the volatility of a given ...
Related Articles
  1. Trading

    Exploring the Exponentially Weighted Moving Average

    Learn how to calculate a metric that improves on simple variance.
  2. Trading

    Implied Volatility: Buy Low and Sell High

    The success of an options trade can be significantly enhanced by being on the right side of implied volatility changes.
  3. Trading

    The Anatomy of Options

    Find out how you can use the "Greeks" to guide your options trading strategy and help balance your portfolio.
  4. Trading

    Option Price-Volatility Relationship: Avoiding Negative Surprises

    Learn about the price-volatility dynamic and its dual effect on option positions.
  5. Trading

    An Option Strategy for Trading Market Bottoms

    A reverse calendar spread offers a low-risk trading setup with profit potential in both directions.
  6. Trading

    Understanding Option Pricing

    This article will explore what factors you need to consider in the pricing of options when trying to take advantage of a stock price's movement.
  7. Trading

    Stock Options: What's Price Got To Do With It?

    A thorough understanding of risk is essential in options trading. So is knowing the factors that affect option price.
  8. Trading

    Ratio Writing: A High-Volatility Options Strategy

    Selling a greater number of options than you buy profits from a decline back to average levels of implied volatility.
  1. What is the relationship between implied volatility and the volatility skew?

    Learn what the relationship is between implied volatility and the volatility skew, and see how implied volatility impacts ... Read Answer >>
  2. Which market indicators reflect volatility in the stock market?

    Learn the most commonly used technical indicators of stock market volatility that are watched by stock market traders and ... Read Answer >>
Hot Definitions
  1. Compound Annual Growth Rate - CAGR

    The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer ...
  2. Net Present Value - NPV

    Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows ...
  3. Price-Earnings Ratio - P/E Ratio

    The Price-to-Earnings Ratio or P/E ratio is a ratio for valuing a company that measures its current share price relative ...
  4. Internal Rate of Return - IRR

    Internal Rate of Return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments.
  5. Limit Order

    An order placed with a brokerage to buy or sell a set number of shares at a specified price or better.
  6. Current Ratio

    The current ratio is a liquidity ratio that measures a company's ability to pay short-term and long-term obligations.
Trading Center