Lambda is the lesser known Greek value that may be the key to understanding option leverage.

Introduction to Lambda and Leverage

What is Lambda?

I came across something I wanted to share recently when exploring some of the different financial calculations commonly used for options. The finding is a Greek value called Lambda and it can be used to measure option leverage. The following link gives Lambda’s definition according to Investopedia:

Investopedia’s Definition of Lambda

The Basic Greeks

As options traders, we’re all pretty familiar with the Greeks. Generally speaking, they give us estimates of how option contract prices will react to different events:

Delta - measures reaction in option price in relation to movement of underlying stock price

Gamma - measures change in delta as price of the underlying stock changes

Theta - measure decay of option price per day as time moves closer to expiration

Vega - measures reaction in option price in relation to change in implied volatility

Rho - measures reaction in option price in relation to change in interest rates

We use these to determine our approaches in purchasing as we think about things like price action, volatility and interest rates etc. and they work very well but they don’t tell the full story still.

Calculating Lambda

An extremely useful but less known Greek value is the measure called Lambda. Lambda, also called an option’s elasticity, measures the ratio of exposure given by purchasing an option contract. Its value tells you how much you can expect the option contract to appreciate per 1% of appreciation of the underlying stock.

Essentially it’s exactly what most of us want to know when purchasing our different calls/puts but is not shown because it’s expected that people can derive the value using the other Greeks.

Since not everyone is trying to do a bunch of math I’m not expecting people to know this and therefore many might not be aware of it. Nonetheless it is a very straightforward calculation that can help you when determining how best to leverage/hedge yourself:

Lambda = Delta * Stock Price / Option Price

Example Calculations

Example 1

JAN 2022 CVS $45 LEAP Call Contract

For example let’s look at a 2022 LEAP on CVS that is currently sitting with a strike price of $45 and costs $14.68 based on midpoint of ask and bid. The delta shown is 0.8368 and the current market price of CVS is $57.82

Lambda = 0.8368 * $57.82 / $14.68
Lambda = 3.296

This means that for every 1% movement in CVS, this particular option will gain (or lose) 3.296% in the same direction since it’s Lambda value is positive

Example 2

DEC 2020 TSLA $480 Put Contract

Let’s look an an example using a TSLA put option for December expiration this year at strike price of $480 that currently costs $108.63 based on average of bid and ask. It has a delta of -0.5619 and TSLA market price is sitting at $411

Lambda = -0.5619 * $411 / $108.63
Lambda = -2.126

This means that for every 1% of movement in TSLA, this particular option will gain (or lose) 2.126% in the opposite direction since it’s Lambda value is negative

Conclusion

Using Lambda, you can quickly see how much leverage or hedging is available in your options choices and can help you when determining how to play your strategy. Good luck and let me know if there’s any questions!