Volatility arbitrage. I remember being very intimidated when I first heard this term being thrown around in trading. Once I learned more about it, however, I realized that it was more or less just a fancy way of saying what many options traders do for a living. This general introduction applies to both sell side and buy-side/proprietary traders.
So what is volatility arbitrage?
Our good friend Wikipedia says:
Volatility arbitrage (or vol arb) is a type of statistical arbitrage that is implemented by trading a delta neutral portfolio of an option and its underlier. The objective is to take advantage of differences between the implied volatility of the option, and a forecast of future realized volatility of the option's underlier.
Honestly, this definition is pretty good, but let’s define a couple of the terms used for emphasis:
- Statistical arbitrage: This is extremely important first point. Vol arb is not a pure, or deterministic, arbitrage strategy. That means you can’t guarantee that you will make profit from it. Because it is a statistical arbitrage strategy, it requires a lot of capital to make returns and the risk is relatively low (especially relative to the amount of capital used) compared to other types of trading, especially if one executes it well.
- Delta neutral: This is a delta neutral strategy, meaning that you are indifferent (ideally, see below on hedging) to whether the underlying moves up or down in price. You are instead betting on the volatility of the particular option increasing or decreasing
To expand on the concept more (but definitely not completely), I will focus on two aspects of this strategy: hedging and market making. What I will not explain is how a trader decides to go long or short volatility on a given product; this is like asking me to explain “How do you know if a stock will go up or down?” There are too many answers and none of them are 100% correct all the time, otherwise I would be retired on some exotic island enjoying my scotch on the rocks instead of writing this post.
Hedging basics/implications
Here’s a basic example to describe how one executes a volatility arbitrage strategy. Let’s assume that I have a view (completely hypothetical, don’t go trade this and then blame me) that the TSLA March 14 155 Call is cheap; that is, its implied volatility is lower than what markets will realize empirically. Because I think the implied volatility is low, I will buy this option, say 75 contracts. This option has a delta of 0.4559 (as of market close 7/26/13), so to hedge my delta risk, I will need to sell 75 x 100 x 0.4559 = 3419 shares of TSLA.
This delta neutral position is only valid at the time of trade because as some of you may know, many things can happen in the market to make it so that your position is no longer delta neutral, the most important of which is gamma, which defines how an option’s delta changes with respect to the underlying price. How often you “gamma hedge” (re-hedge so that your position is delta neutral) throughout the life cycle of your position as the underlying moves up and down is a decision that all traders have to make, whether discretionarily or systematically through a hedging algorithm. This decision will greatly impact PnL in volatility arbitrage because it affects how “pure” the volatility arbitrage is (how delta neutral the position is).
Market making
In my opinion, this is one of the most interesting parts of volatility arbitrage, and there is a lot more information about it than what I’ll post here. Like above, I will give an example that hopefully demonstrates the role volatility arbitrage market makers have in today’s markets.
A buy side firm wants to buy 250 GOOG calls (let’s say delta = 0.50 for simplicity’s sake) to express their bullish view on the stock. I am an option market maker who is neither bullish nor bearish on GOOG but believes that these particular options’ volatility is too rich, so I sell the 250 GOOG calls to this firm (I am now short GOOG) and buy 12500 shares of GOOG to hedge my delta. Two weeks later (assume that I have hedged my deltas during this time), GOOG stock increases by 5% and coincidentally, GOOG vols also fall. In this scenario, both my counterparty and I made money in this trade. Isn’t that nice? :) This is the beauty of an option market maker at work.
Imagine if in this situation, I did not have a view on volatility but instead also had a bullish or bearish view on the underlying. Then to engage in this trade would be tantamount to me, an aspiring trader in his mid-20s, saying that this experienced portfolio manager from a prestigious/successful fund is wrong and that I am right (since the trade would be a zero-sum game). I'm glad that I don't have to make those kind of decisions at work.
Hope this was helpful. Feel free to add more thoughts/comments!
Good to see more trading posts on this site. Thanks!
Great post, thanks!
How often/at what gamma value would you adjust your positions to reflect new gamma values (re-hedging)? I realize there isn't an exact answer, but what's a ballpark figure that the hedging algorithms are waiting for?
Like you said, it depends, and often this value is configurable by product/symbol. Also, I think it makes more sense that most of these algos just look for large enough delta to hedge (since it theoretically should be zero).
Awesome!
Could you explain what the implied vol number means? Its always quoted as a percentage, but I have no idea what it actually means
The Black-Scholes model for option pricing has a set number of inputs: price of the underlying (or spot price), strike price of the option, time to maturity of the option, the risk free interest rate, the volatility of the option, and (possibly) the dividend rate of the underlying. With these inputs, one can calculate the theoretical price of the option in question.
However, in the real world, the market shows us how much the option costs. The idea of implied volatility is that if you take that market option price and put it back into the Black-Scholes model, you can solve for the other unknowns, in this case the volatility. Therefore, the volatility "implied" by the market price of an option is called the implied volatility. Technically, this doesn't even have to be done by the Black-Scholes formula; any theoretical option pricing model can yield an implied volatility.
Thanks man, but what I really meant was what the number actually meant? For example an option I was looking at was quoted at 140 implied vol. How is that different from lets say 90?
A higher implied vol says that the market is pricing in greater standard deviation for the underlying's price moves.
For example, if you have an implied volatility of 90%, about 2/3 of the time (roughly one standard deviation), the underlying will be between -90% and +90% in one year. Since this number is annual, you can also calculate similar statistics for monthly, daily, etc.
On a related note, this is sometimes how traders estimate realized volatility. They have a good gauge of how much the underlying moves on a single day on average, and multiply that % by 16 (roughly the square root of 252, number of trading days in a year) to find the annualized realized volatility to compare to the market implied volatility.
What if your view of GOOGs vol is that it is too low? Is it still possible to make a play on that given that your counterparty is going long GOOG calls?
Or what if you have no opinion about their volatility? Doesn't the fact that you are short the option necessarily imply that you are short vol?
I know that I'm missing something, probably involving offsetting puts, am I on the right track?
Like, I totes love this post, shit show chart, and timing, peyo212/nonchalant smurf +1sb
Thank you peyo212. It's a great work. I see from above discussion that a trader can estimate the realized volatility. But, how does a trader get implied volatility information so as to compared realized volatility and implied volatility?
volatility and index arb? (Originally Posted: 06/27/2008)
Can anyone share information on 1) index arbitrage trading 2) volatility index arbitrage trading
Specifically: what does the trader on a typical day? Is it mostly just hedging? And how is the pay like?
There seem to be a lot of threads on FX/Rates/Credit/Commodities but very few on these two areas, and I would appreciate any input.
Humans don't work on arbitrage trading anymore. It's done by computers now. Of-course, the traders on this desk usually make sure the computer isn't trading too aggressively or too impassively.
Thanks indian-banker. So there is not much demand for people in these two areas?
Are there any new/emerging areas in trading that involve indices? Or is it mostly just in arbitrage?
People do work there but it's usually people who are good with programming etc. I'm not really sure what new areas there are involving indices. People do trade CDS indices a lot but that's not new. You have the CDX north america, itraxx etc...
Thanks indian-banker - I sent you a PM.
sorry for being off topic here, but i was just wondering if u have a spot rate for say gbp/usd and eur/usd u can easily find gbp/eur. How about if u have the implied vols of the first two pairs (and u know the correlation of these is say r)...how do u find the imp vol for gbp/eur?
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