Intra-day volatility arbitrage strategy (VolArb)

[ShinjiOno]

I'm trying to implement a trading strategy, however I'm stuck with "replicating volatility". Hope that you can shed some light on this. Below are all the info that I have gathered about the strategy.

Intra-day volatility arbitrage strategy (VolArb)

It has been long observed (Lo and MacKinlay 1988) that, for a mean-reverting process, the high frequency volatility is bigger than the low frequency volatility, hence an arbitrage opportunity. For instance, the daily volatility > monthly volatility > yearly volatility. Conceivably, we may make a profit by buying the bigger volatility and selling the smaller volatility. In fact, we can mathematically compute the expected P&L for any price process.
The success of the VolArb strategy depends on

• finding or constructing a piece-wise mean-reverting or slowly-moving-mean asset,
• trading the "right" volatility difference(s).

Each of the two topics is an important subject in its own right.
We have extensively evaluated the performance of VolArb on trading currency pairs in many settings, taking into account bid-ask. For low frequency trading, the P&L is above 6% of the maximalexposure with a max draw down of 2 - 3%. The Sharpe ratio ranges from 2 to 3. For higher frequency trading, e.g., intra-day, the P&L ranges from 20% - 40% of the maximal exposure with a max draw down of 2 - 8%. The Sharpe ratio is above 2.


Given any price time series, the volatility changes depending on how often you take an observation. For instance, suppose, for AUDNZD, you use the hourly data to compute volatility (V_H) and the daily data to compute volatility (V_D). You will see that V_H is bigger than V_D statistically. This is a property of any mean-reverting asset/price process, which can be proved mathematically.

So, if you can replicate V_H by buying and selling AUDNZD, and replicate V_D by buying and selling AUDNZD. You are expected to make a profit proportional to (V_H - V_D) > 0.
For a pair (AUDNZD, GBPJPY), the concept is the same. We apply it to the spread adjusted by beta, such as, Z = AUDNZD - GBPJPY. So, we are buying and sell AUDNZD and GBPJPY, according to the volatility difference signal.

Can you please shed a light on how to replicate V_H or V_D?
Did you mean, buy/sell underlying asset at low/high price based on its mean-reversion?
it is about buying/selling the underlying asset(s) at low/high to replicate V_H and V_D.

 

[financeguy]

This is something that sell-siders do regularly. It's just called delta hedging. If you buy options, you'll be long gamma. Dynamically delta hedging the position to delta neutral as spot moves net with the PNL from the option itself on any given day has expected value equal to each day's theta bill. Whether you hedge hourly or daily has the same expected value, but you might observe that a given currency is subject more to hourly mean reverting moves than large daily moves, so you'd elect to delta hedge more frequently. Maybe the currency is trending in one direction so you let spot run further before re-adjusting your delta. You don't need to to it at a fixed interval either, you could just let it be subject to your discretion when you re-hedge. But you will not make as much money re-hedging at every little tick as you would if you let spot run and then hedge over bigger moves (the risk being that if you don't take your profits in time spot might never have a big enough move for you to take profit on and mean revert on you before you get a chance to lock anything in). So if you expect vol to be high, let spot run, and if you expect vol to be low take profit often. This is just consistent with if you think vol will be high, buy options, and sell then if you think vol will be low. None of this really arbitrage, it's just an attempt to be a little clever and use a bit of math to tease a bit more money out of a gamma position.

 

[ShinjiOno]

However, the source states that the strategy buy/sell underlying asset at low/high price to replicate V_H and V_D. Is that possible?

No option involved

 

[financeguy]

However, the source states that the strategy buy/sell underlying asset at low/high price to replicate V_H and V_D. Is that possible?

No option involved

Sure you can do it, and there's also a lot of research done by the sell side on options replication via dynamic spot trading. Basically you trade an imaginary short gamma position which you don't actually have to replicate a long option position. Sort of a mind-fk but think about it and it sort of makes sense. This is mainly marketed to corporates who want option-like exposure but who aren't allowed to actually trade options. So in principle you could do the same thing here, trading imaginary gamma in different styles for two different assets, just bear in mind there's definitely no free lunch embedded in this strategy and in fact is quite risky.

 

[dmv]

looks like something is missed.

how can take any position in gamma via delta one instrument?

difference in vols for different time scales is just an effect of autocorrelation. frequent data is autocorrelated