Volatility calculation using a fair bet approach

Brainstorming about market neutral option strategies I came up with an idea to use the fair bet price approach to calculate volatility.

The fair price of a bet:

The fair price of a bet is when neither the buyer nor the seller of the bet has got an advantage. In the long run it should be a zero sum game game for both.

Think about a simple coin flip game. If you bet on head you can either win 1€ if head is up or nothing if tail comes on top. What would be the fair price for such an bet?

As head and tail got the same probability, the expected return of a bet on head’s up would be 0.5€. If I would sell you a bet on the next coin flip, I would charge you this 0.5€ to make it a fair bet. So you would either lose the 0.5€ if tail’s up, or win 1€ -0.5€ if head’s up. In the long run this would be a zero sum game for both of us.

We could do the same thing for a tail’s up bet. The fair price of this bet would also be 0.5€.

Implied Volatility

If you buy an at the money call and an at the money put you got a straddle. If you are long you win if the market trades outside the current price +/- the price for the straddle. You win, if the market trades inside these boundaries and you are the seller of the straddle.

The price for the at the money straddle is called implied volatility. It is set by supply and demand and will be the fair price for expected market volatility until expiry ot the options.

Historic Implied Volatility

We will not be able to calculate which volatility the market expects for the upcoming days, but we can calculate what the fair price for a straddle over the past period of data would have been. Comparing this number to the actual implied volatility can give some insights into the question if you would like to have a long or short straddle.

Historical Implied Volatility KVOL:

Historical volatility uses standard deviation of daily log returns to describe the volatility of the market. The standard deviation of this +1 -1 coin flip experiment would be 1€. The same would be true if you would buy a head’s up and a tail’s up bet; it would also cost you 1€. So for this simple example the fair bet based volatility is the same as the historical volatility.

But the market is not a coin flip. There will be some differences between historical volatility and KVOL fair bet based volatility.

KVOL vs. historical volatility:

The chart shows you a comparison between KVOL (blue) and historical volatility (standard deviation). On the chart shown above both calculate the volatility for 10 day returns, using the previous 30 bars as data sample.

As you can see historical volatility and KVOL are highly correlated.

But there are some major differences:

As an example in the end of 2017/beginning of 2018 KVOL starts to rise as the market is exploding to the upside. This is due to the virtual call used to calculate KVOL gains value. At the same time historical volatility stays low, as the market has got one direction and no setbacks.

Another advantage of KVOL is it`s response to singular events. As you can see on Sept. 3rd on the chart above the singular big red candle leads to a spike in historical volatility. It also raises KVOL, but not as much. As both indicators are calculated over the same period of bars they both got the same speed of change, but when you have a look at the scale you will see the advantage of KVOL: Historical volatility jumps from 0.2 to over 0.5 – it more than doubles just because of a single event. KVOL also raises,but only from 0.2 to 0.3.

For me this mild response to to singular events is the main advantage. Imagine a portfolio based on value at risk – would it really be useful to half the exposure just because historical volatility jumps after a single red candle?

KVOL  – Tradesignal Equilla Code:

The code to calculate KVOL is simple and straightforward.

The inputs:

multi: just a multiplier, like you can display 1 or 2 standard deviations..

datapoints: The number of bars used to calculate KVOL

returnperiod: calculate the volatility for 1,2,3… bars

showresult: show the result as a percentage of the underlying or as an absolute number

Stay tuned for some examples what can be done using this volatility measure…