# Tracking realized volatility

#### elfopposwe

Hi everyone

I'm taking my first steps from academia to industry and could use some advice on some matters regarding the calculation of actual or realized volatility
.
I'm backtesting a volarb (statarb) strategy and need to track realized volatility. I have thought of two ways of doing this, but I could really use some ideas and input on them both.

First method:
The "ordinary" calculation, using
16*sqrt(sum[ln(Rt/Rt-1)^2] / N)
over some period of N observations. (16=sqrt(256) being an approximation of sqrt(252), scaling daily to yearly vol)
My issue is what window to use? One aim is to track the difference between implied and realized volatility on a daily basis, so the ideal situation would be to measure the actual "true" daily volatility. Since that isn't possible, is there some industry standard way to measure the realized volatility each day?
I should add that I only have access to end-of-day quotes at the moment, but feel free to give your thoughts on suitable data!

Second method:
In the world of stochastic calculus we can show that, for a process defined by
dS = mu*S*dt + sigma*S*dz (the ordinary stock process)
and as dt approaches zero (sufficiently small time steps), we have
(dS)^2 = S^2 * sigma^2 *dt
where "sigma" is the volatility affecting the process, i e the actual realized volatility, and dS=S(t) - S(t-1). If this is true, I could use this expression each day when calculating dPi (change in portfolio value each day).
The problem I have with this is that it, being based on one single dS value, is very volatile. An immediate question is "is dt=1d (day) sufficiently small?", and can we even use this in practice? Warning bells start sounding when I read "as dt-->0"... =)

What I would really like is to show empirically that the two methods approach each other for some particular N-window (first method), but the (dS)^2-values are all over the place.

Any ideas or other points of view?

#### Springer

Hi elfopposwe, if you're aiming to measure integrated vol you've answered yourself and you'll need to use tick data; the usual way we calculate realized vol. If all you have are close to close prices your calculated realized vol will be too wild. Either use a filter with something like the HRS model, or Parkinsons or other measure.

#### HyperVolatility

It is wise using a combined approach. Try to mix parametric models (Heston,SABR,Garch) with nonparamentric vol models (Parkinsons,close-to-close) and then contrast the outcomes.

Do not use only 1 measurement because a single model will be never be sophisticated enough to capture all the patterns or to extract all the info that you really need.

For instance, if you use a stochastic model with jump diffusion for a stock whose prices is "dominated" by jumps the outcome will be pretty reliable but for a low vol stock this is not going to be good because the model will assume that the path followed by th price is jumps-dominated. Clearly, in the last case a close-to-close vol model would be more than fine.

There is no simple answer when it comes to volatility.If you are using these models to trade do not get involved in the "how we get things more complicated" challenge.

A more difficult model is not going to give you a particular edge over the crowd. In real life, MORE DIFFUCULT DOES NOT MEAN MORE PROFITABLE !!!!

I discovered that when I first moved from academia to trading.When I was at uni I thought: "ok, this model is more complicated so it must be worth the pain" but later I realised that the time and efforts required to use those models was not rewarded in terms of portfolio returns. Good Luck

#### elfopposwe

Springer, thanks a lot for your input and suggestions on possible solutions!

It is wise using a combined approach. Try to mix parametric models (Heston,SABR,Garch) with nonparamentric vol models (Parkinsons,close-to-close) and then contrast the outcomes.

Do not use only 1 measurement because a single model will be never be sophisticated enough to capture all the patterns or to extract all the info that you really need.

For instance, if you use a stochastic model with jump diffusion for a stock whose prices is "dominated" by jumps the outcome will be pretty reliable but for a low vol stock this is not going to be good because the model will assume that the path followed by th price is jumps-dominated. Clearly, in the last case a close-to-close vol model would be more than fine.

There is no simple answer when it comes to volatility.If you are using these models to trade do not get involved in the "how we get things more complicated" challenge.

A more difficult model is not going to give you a particular edge over the crowd. In real life, MORE DIFFUCULT DOES NOT MEAN MORE PROFITABLE !!!!

I discovered that when I first moved from academia to trading.When I was at uni I thought: "ok, this model is more complicated so it must be worth the pain" but later I realised that the time and efforts required to use those models was not rewarded in terms of portfolio returns. Good Luck

Hypervolatility, thanks for your reply. Your good advice about keeping it as simple as possible brings up the question of how simple we can keep things. Let me explain a bit more about what I'm trying to do:

I'm trying to empirically prove the PnL of a volarb strategy by calculating it in 2 different ways to (hopefully) find approximately the same results regardless of calculation method.

1: The strategy involves a delta-hedge straddle. For such a portfolio we can derive a formula for the change in portfolio value (dPi), where dPi is dependent on the difference between implied and realized volatility. This is where I need to track realized volatility, and this is what my initial question was about.

2: We can also use mark-to-market each day to value the portfolio and note the portfolio change.

Method 2 is straightforward, method 1 is not (for me, anyway :P). Is this a typical case where I would need to, as you mentioned, mix parametric and nonparametric models and contrast the outcomes? Or, (thinking of your advice "If you are using these models to trade do not get involved in the 'how we get things more complicated' challenge) should I keep it even more simple than that? You're probably right about not only using one measurement so the question now is how sophisticated I need to keep things... after all, I am just trying to find a good view of whether the strat is profitable or not when trading it for real.

#### HyperVolatility

If you are going to follow the mark-to-market approach you are going to miss information. Should you simply want to see how P&L changes you can just run a Monte Carlo Value-at-Risk and look at potential outcomes.(if this is what you want. im sorry but you dont make it clear in your previous post)

1) "method 1 is not (for me, anyway :P). Is this a typical case where I would need to, as you mentioned, mix parametric and nonparametric models and contrast the outcomes?"

yes, that's what I was referring to.

2) "thinking of your advice "If you are using these models to trade do not get involved in the 'how we get things more complicated' challenge) should I keep it even more simple than that?"

No, because getting a simpler measurement of volatility would give you a rough outcome. you'd better off using models like Heston or an asymmetric GARCH model (I would recommend the TGARCH or the EGARCH ) and contrast the outcomes against the Parkinsons model and the close-to-close method.

The Heston is good because it takes into account the volatility of volatility

The asymmetric GARCH models are good because they introduce a mean-reverting parameter towards which the volatility tend to collapse to and,as we all know, volatility is mean reverting.

Parkinson and close-to-close methods capture a different "side" of the market because they are based on real prices and are not parametric. Even if you use returns in the close-to-close method you are not calibrating the model since no parameter estimator such as OLS, MLE or QMLE is adopted.

Once you get all the outcomes you can then see which one is the most appropriate.

If you need further details drop me a private message because I trade using pretty much the same approach and it would be interesting sharing ideas.

Hope this helped

www.hypervolatility.com

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