Risk: Asia-specific Vix indexes fail to ignite market interest.

The title pretty much says it all, that outside US and VSTOXX on Eurex volatility futures have not taken off. Will this change now since CBOE introduced (almost) 24-hour trading in VIX futures? Will arbitrageurs add liquidity to Asian products, or will Asian hedgers flock to VIX to manage risk? Only time will tell.

# Volatility Futures & Options

## Jun 27, 2014

## Jun 19, 2014

### More Intuition On Volatility And Square Root Of Time

Vance at Six Figure Investing recently wrote an excellent post titled Volatility and the Square Root of Time. I would like to try to add a little more intuition about this particular theoretical property of gaussian random walk process, or Wiener process.

If we gloss over technical details Wiener process can be described as a sum of random draws from normal distribution - that is starting at 0 we keep adding a new random number at each time step. However we are going simplify this even further, and will use even more basic process - starting at 0, at each time step we flip a coin, and with heads we add 1, with tails we subtract one. And although this may sound like a grade-school version of Wiener process this is actually a valid "substitute" for our purposes.

Here I plotted some sample paths. And yes, this binomial walk looks quite like gaussian random walk.

Now we will look at the process in greater detail, and specifically we will look at the volatility of the process at each time step.

So, we take the first step, and calculate expected variance as sum of squared values multiplied by probabilities. In this case we get (1)

After 2 steps we have 3 values, and 4 distinct paths: +1 + 1 = 2, +1 -1 = 0, -1 + 1 = 0, and -1 -1 = -2. We use the same method to calculate variance: (2)

After 3 steps we have 4 values, and 8 distinct paths which I am not going to enumerate; count for yourself. We use the same method to calculate variance: (3)

As you can see variance scales with time, while volatility scales with its square root. I should point out that volatility is not the only quantity to scale with the √t, the property also holds true for expected high, expected low, expected range, expected drawdown and drawup - they all scale the same way, as I wrote in another post.

Finally, Vance writes that the relationship approximately holds for options (assuming no rates and no dividends). I would clarify: it holds approximately assuming small rates, small dividends, and small volatility. Also it holds much better for ATM options, but not so much when you move away from the money.

If we gloss over technical details Wiener process can be described as a sum of random draws from normal distribution - that is starting at 0 we keep adding a new random number at each time step. However we are going simplify this even further, and will use even more basic process - starting at 0, at each time step we flip a coin, and with heads we add 1, with tails we subtract one. And although this may sound like a grade-school version of Wiener process this is actually a valid "substitute" for our purposes.

Here I plotted some sample paths. And yes, this binomial walk looks quite like gaussian random walk.

Now we will look at the process in greater detail, and specifically we will look at the volatility of the process at each time step.

t=0 | t=1 | probability |
---|---|---|

+1 | ½ | |

0 | ||

-1 | ½ |

^{2}* ½ + (-1)^{2}* ½ = 1. So, t=1, variance=1, volatility=√1=1 . Ok, onet=0 | t=1 | t=2 | probability |
---|---|---|---|

+2 | ¼ | ||

+1 | |||

0 | 0 | ½ | |

-1 | |||

-2 | ¼ |

After 2 steps we have 3 values, and 4 distinct paths: +1 + 1 = 2, +1 -1 = 0, -1 + 1 = 0, and -1 -1 = -2. We use the same method to calculate variance: (2)

^{2}* ¼ + (0)^{2}* ½ + (-2)^{2}* ¼ = 1 + 1 = 2. So, t=2, variance=2, volatility=√2 . Ok, let's do one more step:t=0 | t=1 | t=2 | t=3 | probability |
---|---|---|---|---|

+3 | ⅛ | |||

+2 | ||||

+1 | +1 | ⅜ | ||

0 | 0 | |||

-1 | -1 | ⅜ | ||

-2 | ||||

-3 | ⅛ |

After 3 steps we have 4 values, and 8 distinct paths which I am not going to enumerate; count for yourself. We use the same method to calculate variance: (3)

^{2}* ⅛ + (1)^{2}* ⅜ + (-1)^{2}* ⅜ + (-3)^{2}* ⅛ = 9/8 + 3/8 + 3/8 + 9/8 = 24/8 = 3. So, t=3, variance=3, volatility=√3As you can see variance scales with time, while volatility scales with its square root. I should point out that volatility is not the only quantity to scale with the √t, the property also holds true for expected high, expected low, expected range, expected drawdown and drawup - they all scale the same way, as I wrote in another post.

Finally, Vance writes that the relationship approximately holds for options (assuming no rates and no dividends). I would clarify: it holds approximately assuming small rates, small dividends, and small volatility. Also it holds much better for ATM options, but not so much when you move away from the money.

## Apr 1, 2014

### India VIX

India VIX futures launched little over a month ago (exchange brochure, quotes) , and I am cautiously optimistic. The contract is straight-forward, but expiration dates are unusual - National Stock Exchange of India currently lists three weekly contracts expiring on Tuesdays, e.g. right now available contracts are Apr 1 (just expired), Apr 7 (moved day earlier because of exchange holiday), and Apr 15. Tomorrow NSE will list Apr 22 contract.

I checked bloomberg few hours ago, to follow up on other volatility futures, and here are today's numbers:

Unfortunately, it looks like most of the international volatility futures did not take off. VNKY looks solid, but volume still disappoints. India VIX is still in a honeymoon period; let's hope the volume stays.

I checked bloomberg few hours ago, to follow up on other volatility futures, and here are today's numbers:

Volume | Open Interest | |

VNKY (Nikkei) | 232 | 1091 |

INVIXN (Nifty) | 692 | 497* |

RTSVX (RTS) | 0 | 8 |

SPAVIX (S&P/ASX 200) | 0 | N/A |

VHSI (HSI) | 0 | 12 |

Unfortunately, it looks like most of the international volatility futures did not take off. VNKY looks solid, but volume still disappoints. India VIX is still in a honeymoon period; let's hope the volume stays.

* open interest as reported by NSE stands at 372750, but I believe that number is OI * 750 (contract size) I reported adjusted number for consistency.

## Jan 7, 2014

### VIX, VIX Futures, and VIX ETNs - Interview with John Hwang

John “Hojun” Hwang is the author of VIX, VIX Futures, and VIX ETNs , a conceptual guide to trading the VIX index. He graduated with degrees in Computer Science and Mathematics from Stanford University, where he spent summers working at Symantec and Goldman Sachs. Afterwards, John joined Morgan Stanley as a quantitative trader. In 2009, John was recruited into U.S. index derivatives trading, where he was responsible for managing VIX index products, variance swaps, and structured volatility vehicles. Since 2013, John has managed his own firm, Silvertrend, LLC, that focuses on technology trends and online businesses. He can be reached with questions about his book or the VIX index at author@vixanalytics.com

**OnlyVIX**: Tell us - how did you get started in finance?

**John Hwang**: I learned about finance after taking an econometrics course in college. The idea that one can apply quantitative methods to model stock market behavior really fascinated me. Afterwards, I started dabbling in forex trading, which I discovered through online communities. Then, at the end of my junior year, I found a job posting for a summer internship at Goldman Sachs’ Fixed Income, Commodities, and Currencies division (FICC). I was fortunate enough to get in, which helped kickstart my career.

At Goldman Sachs, I rotated through research, spot FX trading, index derivatives, and exotics trading desks. Afterwards, I realized that I was interested in index derivatives the most. I still vividly remember to this day when a Nikkei 225 options trader sat me down to teach me how to trade skew. He drew the Nikkei 6 month skew on a paper napkin, and showed me at least six different ways to express a skew flattener. Immediately afterwards, he actually traded a risk reversal in the over the counter market. That made a big impression on me. To this day, I don’t know of any profession that allows you to convert an insight into action faster than that.

Also, the multi-dimensional nature of derivatives trading really interested me. At the time, I thought the only way to make money was through taking directional bets. I found taking views on the velocity of the market just as interesting as predicting its direction.

**OV**: How did you get involved with trading the VIX index?

**JH**: I first got involved with the VIX index at Morgan Stanley in the beginning of 2009. I was recruited by the head of variance swap trading to help build out the VIX index business. Volatility exploded in 2008, and there were a lot of funds going under at the time because of ill-placed volatility bets. There was a lot of blood in the VIX index market as well, and many funds had lost their shirts selling convexity.

The VIX index market was pretty fragmented at the time, and there were only a handful of traders on the street specializing in the VIX index. VXX ETN was just getting launched by Barclays. Therefore, the field was rich with research ideas, and I spent a few months writing code to monitor VIX prices and signals. Being able to both code and trade was a big advantage at the time. Afterwards, I was put in charge of trading the VIX index book as well as short dated variance swaps.

**OV**: How was the market different then?

**JH**:In January 2009, no one really believed that the product could make big money, and the success of VIX futures and options has far-exceeded people’s expectations. Since 2009, I saw the business become increasingly electronic, and this helped me see that VIX futures will become immensely popular. VIX futures are great, because they reduce the dimensionality of options, and make betting on volatility really simple. I always believed that vanilla options were too complicated for most retail investors, and there was a big need for simpler products. Since the markets always favor simplicity and transparency, I felt like that was the future of the business.

Indeed, in 2009, VXX and VXZ were launched, and the rest is history. Nowadays, the vega exchanged on VIX ETNs and VIX futures eclipses that of the entire listed market, and VXX is now one of the most actively traded ETFs on the planet.

**OV**: When was the first time you realized the power of VIX futures/VIX options?

**JH**:Watching volatilities spike during the Flash Crash of 2010 was quite an experience. It was definitely the fastest volatility spike that I’ve seen as a VIX trader, and certainly the most violent. I remember May’10 futures gapping 2,3 dollars every tick. When the S&P futures broke 1,100, all hell really break loose. For example, it was the first and only time I have seen the electronic quotations for VIX options disappear entirely. This is remarkable, given that CBOE is usually very good about keeping electronic quotations liquid for most garden-variety crashes. Not only that, I remember the bid ask spreads for futures widening to couple dollars. VIX futures have been hyper-liquid in the previous few years, so you could imagine my astonishment. Fortunately, I ended up doing great that day, because I had covered most of my short strikes in the early morning, and rolled down my out-of-the-money long strikes to get longer volatility.

In some sense, traders had plenty of opportunities to cut longs or even reverse short on that day. The tape was really weak throughout the day, and volumes were accelerating on down moves. People were perhaps caught off guard, because the market had already sold off quite a bit the day before. You could tell by the number of stops that got triggered for S&P futures, especially at the 1125 and 1100 levels. After those levels broke, the market just capitulated pretty hard.

One another event that impressed me was the great melting of skew in early 2009. After the 2008 crash, the market priced in apocalypse type scenarios. At one point, the pessimism reached such heights that it was pricing in a fairly high chance of S&P 500 going to 300 by 2009. That year taught me that much money can be made from both the long and short sides of volatility.

**OV**: What would you say are the two lessons everyone should learn from those events?

**JH**: The first lesson is that systems can become very fragile without notice, by definition. The shock events from 2008 to 2011 probably forced many risk managers to become even more conservative in terms of managing tail risk. You can see even nowadays, even after a few great years in the market, there are many people who take an extremely cautious approach to trading volatility.

Second, I’d mention the importance of not overestimating liquidity in crisis situations. I believe that much of the volatility premium exists simply to compensate for poor liquidity for volatility sellers during shock events. I would also add that liquidity matters whether you are long volatility or short volatility: if you’re long, monetizing gets trickier with poor liquidity. But obviously, you would rather be long than short during those events.

**OV**: Why did you decide to write a book about VIX derivatives?

**JH**: I wanted to write an easy to understand book on the VIX index, because I thought VIX futures tend to be incorrectly utilized and understood by many people. Because they are so simple to trade, it's tempting to not do the homework. I also thought it was my responsibility to write a book in this field, because I remembered how difficult it was for me to obtain information about the VIX when I got started.

Also, VIX futures and VXX have created a new segment of investors who have no prior options background. From my experience, some options knowledge and fundamentals are required for trading VIX futures and VXX. That's why I wrote a book that tries to tie some basic intuition behind options trading with VIX futures and VXX. I want to keep improving the book, so please send me feedback or suggestions to author@vixanalytics.com

**OV**: What happens when investors don't know about option-like properties of VIX derivatives and trade them like other linear instruments?

**JH**: At the minimum, traders should be aware of the natural skew and kurtosis properties of trading volatility. It is hard to see these things in action since 2011 as much, but it's definitely out there. They should understand that the fundamental distribution of returns is different, and why. Also, they should understand the term structure dynamics of volatility.

**OV**: I assume you cover these important subjects in your book

**JH**: Yes, my goal is to educate people to a point where they are not blindly speculating based on historical data. For example, I have seen people contemplating 50%, 60% allocations to short volatility, based on the argument that volatility tends to perform poorly on a historical basis. I’ve presented an alternative framework in the book why that’s not the best way to think about position sizing with the VIX index. At the least, people should realize that many of the popular VIX index trades are highly correlated to risky assets, and the so called ‘risk-on’ trades. Although we are living in a macro regime that rewards leverage and risk-asset plays, it would be foolish not to consider the risks.

**OV**: That is an interesting point. People look at VXX and say - all it did was lose 99% of its value. But the story is obviously more complicated than that ...

**JH**: Exactly. My goal with the book is to educate people enough so that they understand the drivers of VIX futures performance. I try to explain everything in plain English, because I believe that it is unnecessary and even confusing to use complicated models to explain the VIX. In general, I think most complicated concepts can be explained in plain English.

**OV**: What do you see in the future for volatility products, including international volatility futures?

**JH**: I think any good trading vehicle must have the following characteristics: 1) liquidity, 2) transparency (which is a requirement for liquidity), and 3) economics. Fundamentally, these factors require building trust with end-users, whether they be speculators, hedgers, or investors. I believe options are inferior to VIX in terms of liquidity and transparency. If you thought VIX liquidity was bad during crisis events - options liquidity was much worse. VIX is just a more liquid, deeper product, not to mention lower commissions, adjusted for vega. Also, one does not need really complicated tools to trade the VIX, which is a big plus for retail investors.

Regarding international volatility products: I think it's a function of client interest, and it's a chicken and an egg problem. If VSTOXX options are not liquid, client interest will remain low, and tougher for banks to promote. But overall, I’m bullish for increasing adoption of VIX products globally.

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