AD Derivatives Fresh Feature: PDF & CDF SVI Calibrated

Welcome to Amberdata Derivatives Fresh New Features where we go in-depth on features that have recently been built for AD Derivatives customers!

The AD Derivatives Fresh Feature is PDF and CDF, SVI Calibrated, and Breeden-Litzenberger Related.

We’re excited to provide this new feature to all our GUI users. Check it out here!

First, let’s explain what we’re looking at.

Given a well calibrated SVI surface (methodology found here) we can use the parameters to calculate infinite option values and prices for every conceivable strike (we struck an option every 25bps)!

From there we use the Breeden-Litzenberger Formula.

The Breeden-Litzenberger approach relates the second derivative of the call option price with respect to strike price (or equivalently, log-moneyness) to the risk-neutral density function.

Which means we can EXTRACT the option price implied distribution for the underlying, in this case Bitcoin. 

The first chart shows us something that looks like “The Normal Distribution” but because it’s option derived, the market accounts for “Fat Tails” “Skew” and all other failures normal distributions have when applied to markets. 

So it’s the efficient market derived distribution!

From there, we can move away from PDF ("probability density function”) and convert to the CDF (“Cumulative distribution function”). Now we see the terminal probability of the asset being above a certain price. 

In this case, what’s the total density function above $100,000 for BTC at the DEC 27th 2024 expiration? 30% of all observations!

We also have a time-lapse (aka “Shadow” sounds cooler) chart for both the PDF and CDF. Here we can see how the distribution evolved week-over-week! Cool!

Notice that as Bitcoin moved higher the PDF shifted right! Aiming for that $100,000 target! (pew pew) 

Also, notice the distribution peak flattened as implied volatility rose. 

Exciting stuff. 

How is this useful… well it helps traders translate implied volatility into implied probability… traders can then use their subjective assumptions about the market and compare that to what the market is pricing. From there, trade ideas emerge!

Learn more about Amberdata's derivatives offerings here.

Feel free to utilize our AD Derivatives app here.