Last time we looked at implied volatility, we found a close relationship between historical volatility and implied volatility. This time, we want to look at the relative changes of DAX and VDAX and their relationship.

German DAX and VDAX are highly correlated

First, we examine the time series chart of roughly 8 years DAX and VDAX:

 

 

We can see that for each spike in the red curve of DAX, there is an opposite spike in VDAX. This is surprising since we would expect that a large rise in DAX would also cause a large rise in implied volatility, namely VDAX. But, this is not the case. A further investigation is possible using a scatter plot:

 

This scatter plot shows a “x” for all trading days in the past 8 years with VDAX return as x-postion and DAX return as y-postion. This plot shows that there is a close relationship between these two. In fact, a little computation shows that they have correlation of -0.72 which is very high.

What does that mean?

Consider buying a call option: Now, the stock price rises. And the call option price rises because your option is deeper in-the-money: Its asset price minus strike price is higher. But, at the same time, the time value decays because the implied volatility goes down. So, for call option buyers this might be an issue. For Put option buyers, this effect works in their favour. The implied volatility rises when the asset price drops.

By the way, this is a well-known effect: The implied volatility skew. Looking at the traded options, the put options further in-the-money already trade at a higher implied volatility – VDAX represents at-the-money options only.