# Volatility arbitrage

#### volatileN

##### Member
93 0
Hi,

Is anyone here trading any relative value volatility strategies?

I have been looking at some vega neutral calendar spreads where I am long and short different points on the surface for the SPX series.

It seems that there is some great variance / mean reversion in them. I am only using a linear interpolation though - any thoughts on smoothing functions (splines etc) also much appreciated.

Thanks,

VN

#### Robertral

##### Well-known member
446 4
volatileN said:
Hi,

Is anyone here trading any relative value volatility strategies?

I have been looking at some vega neutral calendar spreads where I am long and short different points on the surface for the SPX series.

It seems that there is some great variance / mean reversion in them. I am only using a linear interpolation though - any thoughts on smoothing functions (splines etc) also much appreciated.

Thanks,

VN

Try a multi dimensional non parametric regression

#### anley

##### Senior member
2,730 229
Far too complicated for me to understand!

If I ever want to buy/sell vol then the simplest way is to either buy/short straddles or a safer way is to use a simple delta neutral strategy, ie buy puts and short the index. This though is hard to do on the FTSE because of the size of the future, better to do it on the Nasdaq using QQQs.

#### Thirteen

##### Active member
160 0
Try a multi dimensional non parametric regression

is this a joke dude? how many dimensions are you thinking of? cna you explain this technique?

buying and selling does me sweet.

#### Robertral

##### Well-known member
446 4
Thirteen said:
Try a multi dimensional non parametric regression

is this a joke dude? how many dimensions are you thinking of? cna you explain this technique?

buying and selling does me sweet.

If you are trading off a vol surface you need a smooth surface...hence a multi dimensional non parametric regression is one way of smoothing the surface. It's multi-dim as your vol is a function of time-to-maturity, tau, and strike, X
i.e. vol(tau, X)

Always keep it simple as more parameters means more errors!!!!

#### BBB

##### Experienced member
1,071 3
Quote:
'Always keep it simple as more parameters means more errors!!!!'

True, but you call that simple??

Maybe it's me thats simple?!

#### Robertral

##### Well-known member
446 4
BBB said:
Quote:
'Always keep it simple as more parameters means more errors!!!!'

True, but you call that simple??

Maybe it's me thats simple?!

Well once you've programmed it you can leave it. Put data in and get a vol surface out. No need to think about it again.

The technique is simple yeah, as it's just a bit of stats. We could go complicated and introduce the underlying price in there so that vol is a function of 3 variables, but there is no point at all for the small investor.

I'd be impressed if someone had implemented a REAL-TIME vol surface on a 'normal' PC

#### volatileN

##### Member
93 0
I'd be impressed if someone had implemented a REAL-TIME vol surface on a 'normal' PC [/B][/QUOTE]

I am working on impressing you, hence my search for smoothing functions. It is part of an options package I am building for release later this year. If you have any technical papers on implimentation I would be very grateful.

#### Johnny B. Goode

##### Newbie
5 1
Forgive me if I don't completely understand you strategy but doesn't it rely on the underlying principle that historical vol is a better predictor of future vol than implied vol?

Also, how do you dynamically vega hedge? When do you decide to rebalance?

#### volatileN

##### Member
93 0
Johnny B. Goode said:
Forgive me if I don't completely understand you strategy but doesn't it rely on the underlying principle that historical vol is a better predictor of future vol than implied vol?

Also, how do you dynamically vega hedge? When do you decide to rebalance?

It has nothing to do with the historical / implied vol relationship. Rather it is a stat arb strategy based on assumptions of mean reversion between 2 points on the surface which have got out of kilter relative to their historic values.

I dynamically hedge my vega (and higher moments, dvega/dvol and dveda/dspot) using vanillas.

#### Johnny B. Goode

##### Newbie
5 1

Two things:

1. When you call it an "arb", is it really an arbitrage strategy? Are you buying something in one market and selling its equivalent in another market (Or vice versa)? Is it risk-less with perfect execution? It seems more like you are making a play on perceived mispricings according to projections based on historical vols.

2. I may have completely misunderstood your strategy but when you say "out of kilter with historical values", doesn't this imply that the historical vols (and your projections derived from them)are in some way superior to the implied vols for predicting future vol?

Thanks again. I am very interested in the viability of your approach.

#### volatileN

##### Member
93 0
Johnny B. Goode said:

Two things:

1. When you call it an "arb", is it really an arbitrage strategy? Are you buying something in one market and selling its equivalent in another market (Or vice versa)? Is it risk-less with perfect execution? It seems more like you are making a play on perceived mispricings according to projections based on historical vols.

2. I may have completely misunderstood your strategy but when you say "out of kilter with historical values", doesn't this imply that the historical vols (and your projections derived from them)are in some way superior to the implied vols for predicting future vol?

Thanks again. I am very interested in the viability of your approach.

1) It is an arb in the practitioner rather than academic sense. Compare it to a traditional equity or fixed income stat arb system (pairs trading or whatever you care to call it).

2) When I refer to historical values I am referring to historical levels of implied volatility. Say there is a mean spread between 2 points on the surface of 2% with a standard deviation of 3% and they are currently 8% apart this is 2 standard deviations from the mean. 2% + 3% + 3%. This being the case one would buy the lower point, sell the higher (in such ratios as to make the thing vega neutral), flatten out any delta in spot and await convergence. Typically I would have a stop loss in if it moved another 1 standard deviation and take profits at the mean. This way my gains are always twice (or close allowing for a moving mean) my losses. It is slightly more involved than this but that is the basic theory.

Feel free to shout if my explanation lacks clarity.

Cheers,

VN

#### Johnny B. Goode

##### Newbie
5 1
Shouldn't this be in the Options forum?

Thanks again.

I think I understand what you are doing. A few more questions, if you will allow me.

1. How big of a sample of data do you use in making your historical surface projection?

2. Are you only looking for spreads in vol of 2 or more standard deviations from the mean before you trade? Have you done back-testing on what strategy is optimal for this? (Is it profitable with 1.5 std devs, etc?)

3. Do you scale position size with deviations from the mean spread too?

Thanks again. I really like the idea of your strategy. I am considering programming a system like this and one based on a modified options pricing model (maybe something like Jump Diffusion) to find relative mispricings within and across highly-correlated markets (ie. sp 100, 200 , 500). These appeal to me in particular because I think that they could be done virtually without any human intervention.

volatileN said:

1) It is an arb in the practitioner rather than academic sense. Compare it to a traditional equity or fixed income stat arb system (pairs trading or whatever you care to call it).

2) When I refer to historical values I am referring to historical levels of implied volatility. Say there is a mean spread between 2 points on the surface of 2% with a standard deviation of 3% and they are currently 8% apart this is 2 standard deviations from the mean. 2% + 3% + 3%. This being the case one would buy the lower point, sell the higher (in such ratios as to make the thing vega neutral), flatten out any delta in spot and await convergence. Typically I would have a stop loss in if it moved another 1 standard deviation and take profits at the mean. This way my gains are always twice (or close allowing for a moving mean) my losses. It is slightly more involved than this but that is the basic theory.

Feel free to shout if my explanation lacks clarity.

Cheers,

VN

#### volatileN

##### Member
93 0
Johnny B. Goode said:
Shouldn't this be in the Options forum?

Thanks again.

I think I understand what you are doing. A few more questions, if you will allow me.

1. How big of a sample of data do you use in making your historical surface projection?

2. Are you only looking for spreads in vol of 2 or more standard deviations from the mean before you trade? Have you done back-testing on what strategy is optimal for this? (Is it profitable with 1.5 std devs, etc?)

3. Do you scale position size with deviations from the mean spread too?

Thanks again. I really like the idea of your strategy. I am considering programming a system like this and one based on a modified options pricing model (maybe something like Jump Diffusion) to find relative mispricings within and across highly-correlated markets (ie. sp 100, 200 , 500). These appeal to me in particular because I think that they could be done virtually without any human intervention.

Hi, no problem,

1) When looking at the historical surface data I go back 3 years. We have seen a lot in that time so I consider it to be a fair sample.

2) I have done back testing and run various (linear) optimisation models but have concluded that such curve fitting is dangerous. 2 stdevs does not throw up that many opportunities (by definition) but is very low risk. I might run it on 1.5 if I had a portion of money with a different risk profile as this would (on the backtest) still be very profitable.

3) No, it is always constant.

I admire your quest for a lack of human intervention and am 100% systematic in my approach as well.

As for Jump Diffusion, don't waste your time. It is a nice academic idea (and was ahead of its time in 1976) but it lacks practical application. While assumptions of geometric Brownian motion are obviously flawed the requirements to assume a number of annual jumps and the % of vol explained by those jumps is too abstract.

It is comparable to creditmetrics where people assume a given number of default events. Unfortunately, jumps, like default events are often big, totally stochastic and tend to come several at a time.

I would stick to Black Scholes or, if you have the computational power, a binomial model.

If you do some research on trading discrepancies between highly correlated markets I would be very interested to read it. Correlation is the new volatility :idea: There is a lot of work to be done on it. I am working on a currency option correlation model right now. Trading the correlation between 2 pairs. The beauty is that there is an upper bound (1) and the implied forward correlation often assumes that high values will persist. The attached chart shows otherwise!

#### Attachments

• correlation.doc
31 KB · Views: 453

#### Robertral

##### Well-known member
446 4
volatileN - I'm impressed that your trade volga and vanna, as the effect is so small, I always thought that was more suited to FX book trading where a few mill can be lost for a 1/2 point move in the vanna etc

I will hunt out some papers for you

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