The VXV

It's the CBOE S&P 500 Three-Month Volatility Index. It is from the same family as VIX, but whereas the VIX looks at the implied volatilities of SP500 options of 30 days duration (according to a formula), the VXV looks at the three month picture.

Bill Luby of Vix & More has a good article in Barrons that details how we can use it:

As a result of its elevated profile, the VIX is now followed by a wider variety of investors than at any time in the history of the index. But while the VIX is an important tool, investors -- including those who do not trade options -- would be well-served to look past the VIX for a more nuanced understanding of volatility and its implications for their portfolios.

A case in point is the little-known VXV, whose formal name is the CBOE S&P 500 Three-Month Volatility Index. The VIX calculates implied volatility in S&P 500 index options for merely the next 30 days, but VXV uses a 93-day time window. The different time horizons have some important implications.

You can read the rest of the article HERE.

Where For Art Thou, GS?

"They" let me down yesterday. I will certainly have to brush up on my soothsaying skills I guess.

The employment numbers and the market reaction (a 2 standard deviation move down) must raise the specter of a continuation of the bear market. Most of the credible experts (those that predicted the whole mess in the first place) are incredulous at the up move since March and believe the market should be much lower.

I agree. So when where will the market be manipulated next?

For me, I couldn't give a crap, just don't get there too fast so I can hedge my deltas. VIX ticked up a couple of %, a solid, but not fearful move, so I'm not worried about fast markets... yet, but I don't think we've seen the last of fast down markets.

Disclaimer: I'm delta neutral on the indices.

I'm Buying

OK now that I'm in full conspiracy theory mode, my prediction for today is that GS and MS will have a busy day in the SP pits.

A comment in response to Marketwatch's pre-non farm payrolls numbers:

MarketWatch - why do you pass on this gobbledegook? You guys know as well as all of us that the U.S. government "statistics" are about as dependable as a 2 dollar watch.

...and there are dozens along the same lines.

The payroll numbers will be dreadful, but folk will suspect the government is lying and things are actually much worse (Noooo - who'd believe that?). Folks will realise the bobbleheads optimism is totally misplaced and flog all their stocks the market will open sharply down.

GS & MS will start buying with their ears pinned back for some mysterious account, the market will finish green, Goldilocks will make another cameo appearance, folks will be conned into believing all is well and a return to the upward grind will ensue.

Disclaimer: I'm short gamma on the indices with a little upside skew.

OK I've let my cynicism out for a run, back to normal programming shortly.

Update: As expected, the #s were woeful, now all I need for soothsayer status is for the SP500 to be green by day's end.

Market Manipulated! Levin Lets The Cat Out Of The Bag!

Original Content Sigma Options

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Via ZeroHedge, here is a jawdropping video where Larry Levin let's the cat out of the bag about gu'mint manipulation.

"Larry Levin is a professional futures trader. He has been in and around the S&P 500 futures pit at the largest futures exchange in the world; the Chicago Mercantile Exchange (CME), for almost 20 years.

Larry has been trading his own account or company's proprietary accounts since 1993, trading an average of 2500-3000 E-mini S&P futures contracts a day."

The meaty bit starts at about 2 minutes in.

Covered Calls and Naked Puts - Same Only Different

Original Content Sigma Options

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We all know that naked puts and covered calls are synthetically equivalent... well I hope we all know by now, and we know that a buy write IS a covered call.

My thesis today is that they all may be quite different, not in risk profile, but in the psychology these strategies are a subject of.

Firstly the difference between a covered call and a buy write. Of course there is no official difference, it's long stock and short a call no matter which name you use, but I think there is a difference of inception, the nomenclature different according to the goal of the trader. I think of a buy write as when a stock is bought with the call written at the same time. A covered call I think of as a call written over stock already owned, perhaps for some considerable length of time.

A buy write is entered as a trade to collect the premium (Here I am speaking of general practice, not my practice) and the buy writer is hoping that the stock goes up and is called away. Of course a written put can be used instead, but there are a few reason why the trader doesn't use the naked put. He may have done one of "those" courses. He may not know about synthetic equivalency. His muppet of a broker may not allow him to trade naked puts. This is the sort of trader that scans for high IVs looking for maximum premium (for better or for worse), but he usually doesn't want to keep the stock.

The covered call trader on the other hand, already owns the stock. He probably doesn't want his stock called away, particularly if he has a low cost base and doesn't want a capital gains tax event. As such he is probably writing the call to partially hedge and/or derive some extra income from the premium. His stock is going sideways or perhaps on what he hopes is a short term decline. If the call goes in the money, he is more likely to trade out of the call rather than have his stock assigned.

Please note that these are personal definitions and may not reflects other's thinking.

The naked put trader generally has one of two goals. He either want to just collect premium, so is like our buy writer, or he is writing puts he hopes will end up in the money and wants to be assigned the stock. This second type of naked put trader is more akin, but slightly different to our covered call trader. He is used the puts as part of an overall investment strategy and not really a trader.

All of the above traders may select different strikes and expiries depending on what his ultimate goal is.

So yes, all have the identical payoff diagram when the strike price and expiry are the same, but there are different reasons and psychology that dictate different approaches within the same group of strategies.

Put Spreads - How to Blow Yourself Up In One Easy Lesson

Original Content Sigma Options

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My last few posts have been concentrating of naked puts, the main point I've been trying to get across is that they no more risky than anything else, less so, in fact. But we've seen that they can indeed be a weapon of mass wealth destruction if the trader uses inappropriate levels of leverage.

See:

Naked Puts - Myths & Truths

Naked Puts - An Addendum

Naked Puts - A Horror Story

A suggestion that came up as a safer alternative for a straight out premium collection trade is the bull put spread. In principle, I agreed with the suggestion, but with a few caveats.

1. Proper money management/position sizing is used.
2. Reward versus risk is commensurate with the probability of win/loss.
3. Be careful of correlation with multiple positions.

Even though the bull put spread is perceived as a safer strategy than naked puts, it is not necessarily so, if our old friend leverage is used inappropriately. I would argue that bull put spreads may even be more dangerous than naked puts, depending on the margin requirements of individual jurisdictions and brokerages.

There was an option "education" firm (and I use that term very loosely) in Australia promoting bull put spreads as a panacea for wealth building. The chap even gave it a new name... his name - The ######### Strategy (I have no wish to publicize this rubbish) - how's that for marketing nonsense?

I don't have a challenge with bull puts, 'cept that they aren't appropriate at all times. To borrow a point from Ecclesiastes 3, there is a time for every strategy. The most odious feature of our ersatz options guru is the money management and position sizing algorithm whereby most, if not all of the trader's capital is put at risk in the market. This is spread across four or more positions, but the dearth of tradeable options on the Australian market means there is a very high degree of correlation in optionable stocks.

Every boat rises with the tide, as neophyte bull put traders thought that the Holy Grail had been found at last. That is until the arrival of last year's bear market. Those slow to react, in denial or too green to know what to do next were completely wiped out.

Once again, the fault is not the strategy, the fault is leverage... and fighting the tape.

Naked Puts - A Horror Story

Original Content Sigma Options

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My last couple of posts have been concentrating on removing some of the misconceptions and erroneous assertations regarding the risk of naked puts. I hope I have been carefull enought to stress that you can crank up your risk to unreasonable levels with naked puts. (the same is true of many derivatives).

To illustrate this point, I'm using an example from 2005, because it involved someone I knew.

Background: I had posted up a chart of Elan (ELN:NYSE) in February 2006, on a trading forum I frequent. The stock had been going sideways for two or three months and was trading at ~$27.00. I wanted to get a sense of what folks thought was a good option strategy and generate a bit of options discussion.

Amongst the various replies, one chap said:

Trader: Sell 100 $22.50 puts for about $2000 credit.

Me: That's potentially 10,000 deltas if the stock gets smacked down hard and goes DITM.

Trader: It'll never get there.

The rest as they say, is history.

That's about $143,000 down the pan in one night.

It is important to note that the massive loss is nothing whatever to do with naked puts per se. An equivalent size covered call position would have similar losses, as would a CFD position of similar face value, even more in fact.

The loss was a conequence of "leverage".

I don't know whether the chap took the trade or not, but he was conspicious by his absense on that particular forum from then on. :-(

See:

Naked Puts - Myths and Truths

Naked Puts - An Addendum

Naked Puts - An Addendum

Firstly something a little off topic. It has come to my attention that some media sites have been linking my content onto their sites without my knowledge. I don't mind, it's a bit flattering to be honest, but they haven't extended me the courtesy of attributing the content with a link to this blog such as every blogger does when quoting content. I have no desire to start threatening legal action, so I'll just be putting an embedded link at the top of my posts from now on.

Original Content Sigma Options

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Yesterday I posted up some views on "Naked Puts - Myths And Truths", to which Mark Wolfinger from the excellent Options For Rookies blog, replied in the comments with some very good points I wanted to cover in a new post:

It's not 'being comfortable with the risks' that is the prime consideration.

What is important is for the trader to understand that there is an alternative strategy. Then the alternatives can be compared, and an intelligent choice can be made.

I strongly agree with Mark here. I find it a tad irksome the preponderance of options courses (that charge a rather enormous fee usually) that promote a single strategy as the key to options riches, be it covered calls (the usual) to put spreads, condors whatever. All are really great strategies for a particular market and/or volatility conditions. But no strategy is a catch all, to be applied without considering that there may be a better strategy for the moment.

I prefer selling put spreads. For me, the reduction in potential loss is well worth the reduced profit potential. That's my comfort zone, and each trader should find his/her own.

I have the same feeling in most cases, particularly with individual stocks. As I trade commodity options as well, for me it is not always so. But on stocks I just want to collect premium on, I don't want to be naked at all and also prefer a put spread.

I've moved into the camp that believes that naked put selling is ONLY for investors who want to buy shares as an investment. Traders would do better to use positions that are less risky. That's my opinion - it's not a demand that others agree.

Yes, as I mentioned in the previous post, you have to be prepared to end up with the stock if you trade naked puts. Unless you are happy to be holding the shares for some longer term objective, there are safer alternatives, as mentioned.

My only caveat comes with commodity options. Depending on the situation, based on seasonals, statistical studies, favourable IV etc., I'm quite happy to write naked for a straight out trade. Stuart Johnston covers this very well in his book Trading Options To Win. A great read if folks are into commodity options.

That in no way takes away the validity of Mark's comments however.

The fact that selling puts is less risky than buying stocks, doesn't mean it's a strategy without substantial risk.

Very true. However, if naked puts are risky, it then has to be accepted that long stock of equivalent position size is even more risky. The risk in both can be mitigated, save for humungous gaps.

Also as we know, there are legions of traders who do nothing but trade covered calls with no intention of holding stock long term, yet regard naked puts as the spawn of Satan. My objective was to skewer that misapprehension, arming folks with the knowledge to make more rational decisions. We know the covered call is synthetically equivalent to the naked put and once novice traders get their head around that, it presents them with one of two realisations

1. Folks happy with the risk of covered calls may feel equally happy to trade naked puts of the same face value.
2. Folks realise that covered calls are far more risky than the muppet that sold them a course has told them. I've even seen it claimed that covered calls carry zero risk. :-P

I hope I was careful enough to stress that one can increase their risk of ruin substantially with naked puts by trading too many contracts.

One more point. I don't dislike the idea of naked put selling. In fact, it's one of three strategies that I believe is suitable for rookies. But once the investor has some hands-on trading experience, I suggest moving on to the safer put spread.

I think that's good advice. The caveat being that people can still crash and burn with put spreads. There were a whole host of them I know of in Australia, the followers of one particular "guru" who promoted put spreads as a investing panacea, encouraging people to essentially have their entire capital as risk in correlated underlying stocks. The recent market crash machine gunned those poor folks to pieces.

Option people tend not to talk about money management very much (even specifically disregarded by some "gurus"), and this is paramount with any strategy, no matter how safe it is perceived to be. I think we option people make the mistake thinking that folks have some sort of position sizing algorithm in place. Often they don't and ruin may only be a market swing away with the majority of strategies if the leverage is cranked up enough.

My main point remains, don't be frightened of naked puts, they have their place in the option armoury.

There's plenty there for novices to think about, two slightly differing perspectives but not really that far away from each other.

Naked Puts - Myths and Truths

Naked puts, no strategy is subject to more warnings from ersatz options experts and umm.... educators. Even some very good options people regurgitate some thoroughly dubious statements regarding naked puts. These generally encompass some sort of exhortation to not trade naked puts couched in such beauties as:

1. Naked puts are extremely risky.
2. Naked puts have unlimited risk.
3. Don't ever trade naked puts.
4. Naked puts cause diabetes and heart disease.

OK, I might have exaggerated a bit on the last point, but that is the general tone. All are nonsense without some qualifying conditions. Before I go on, I will point out that naked puts can be very risky if they are traded in a highly risky fashion, and we'll get into that in a moment.

Let's look at this with a bit of basic mathematics.

Naked Puts Are Extremely Risky

Believe it or not, naked puts are less risky than the underlying stock.

Let's take the example of Trader A buying 100 of XYZ common stock @ $50.00 (total outlay $5,000), and Trader B writing a contract of near month naked $50 puts and receiving $2.50 premium ($250 net premium received).

We are not looking at the upside on the stock here, although it should be recognised that the upside is capped at premium received for the option writer, we are looking specifically at risk alone.

At expiry, the put writer pockets the $250 premium no matter what happens to the stock. So if the stock closes @ $50 at option expiry, the option writer is $250 ahead of the stock owner whether assigned or not. Looks like the put writer is a winner in that instance.

What if the stock goes down though?

If the stock goes down, the put writer will likely be assigned and forced to pay $50 for stock that may be worth considerable less. Oh Yeah that's risky! But guess what, the stock buyer is holding stock, bought at $50, that is worth considerable less too. However the put writer has received $250 premium which he keeps, providing a cushion not available to the stock owner.

For example, if the stock is at $40 at option expiry, the stock owner will be down $1,000 at that point in time. Likewise, the put writer will have been assigned the stock @ $50, now worth $40; also a $1,000 loss. But the writer received that $250 premium which means the actual loss is $750.

What seems more risky to you $1,000 loss or $750 loss? The truth is that unless the stock is above $52.50 (in this example) the naked sold put will always be ahead of the stock.

There is another way of looking at this. Lots of folks trade naked puts all the time without ever giving it a second thought, they just trade them synthetically without ever realizing it. Enter the covered call. I have so many people argue with me that a covered call is not the same as a naked put, it's ridiculous. But the mathematics do not lie, a covered call IS a (synthetic) naked put.

Therefore it doesn't make a whole lot of sense to warn about naked puts when folks are completely at ease being long the stock, or long the stock and selling calls over it.

Most of the objections I encounter to this comparison do something like this = "Yeah but, my stop loss will take me out of the stock trade long before it gets to $40". Excuse me? Why is there this presumtion that because a person trades options, they do not have the brains to protect their capital? Options traders can use stop losses too, but it is more likely that they have another strategy in mind e.g. owning the shares or mitigation by adjustment or spreading off.

There are a couple of caveats to the above.

1/ All the above presumes an equal position size. In other words, if we're comparing naked puts to stock, it has to involve the same number, i.e. 100 stock compared to 1 standard option contract (or 1000 in some countries).

2/ Because of the possibilty of assignment, either at expiry or before, you need to have cash in your account to cover the purchase. Furthermore, you have to not mind winding up with the shares and/or have a plan on what to do once the shares are in your account.

There are some traders, through lack of caution or lack of knowledge, or perhaps just a bigger risk profile, who will write huge size out of the money puts, tens or perhaps hundred of contracts in order to collect premium with what they percieve as high probability. The problem is that a black swan event can (and eventually will) blow up those traders spectacularly.

It's proverbially snatching pennies in from in front of a steam roller. If the steam roller catches you, you get squashed. This may be what our option experts try to warn against, but it should be qualified with the actual maths.

Naked puts have unlimited risk

This is my favourite. The word "unlimited" means without limit, infinite. But do naked puts have unlimited risk?

What is the lowest a stock can go? It's zero isn't it? Can a stock go below zero? No, it can't. Therefore we know the maximum loss don't we?

Using the above example, our maximum loss on the naked put is $4,750, that is a $5,000 loss on the stock, less our $250 premium.

Is that unlimited? No!

Is risk unlimited? No! That's just silly.

A better term is "indeterminate risk".

Don't ever trade naked puts

OK don't, seriously! Not unless you are comfortable with the risk/reward profile. But don't not trade them because somebody regurgitated something he heard and never thought about. But if you trade covered calls, there is no reason why you shouldn't trade naked puts instead if you don't already own the stock.

And you shouldn't be afraid to trade them if you know, and are comfotable with the risks.

Of Tribes And Markets

Many centuries ago, a great chief took his son on a journey across the great plain, over two great rivers, across the desert, through the forest whereupon he found a high place. He told his son to look as far as his eye could see and said:

Son, we are Carvetii, this is Carvetii country, and forever more the tribe was known as the Carvetii.

At about the same time another great chief took his son on a journey through a great forest, across two deserts, over a river and to the highest point for 100 miles. He told his son to look as far as his eye could see and said:

Son, we are Cantiaci, this is Cantiaci country, and forever more the tribe was known as the Cantiaci. (These are ancient Briton tribes in case you were wondering.)

Yet another great chief took his son on a great journey at the same time so many centuries ago. He led his son across three plains, across 14 deserts, paddled over 5 lakes, traversed 7 mountain ranges, through 3 forests, across another three deserts, another 2 rivers until he found a high place. He looked at his son and said:

Son, where the Fukawee, and forever more, that people were known as Fukawees.

Centuries later, I am wondering the same thing following the markets convolutions. VIX seems to be moribund, yet is higher than at most times before Sept 2008. Bubblevision boasts of green shoots and recessions ending, yet real world data still indicates death by a thousand cuts. Housing industry vested interests speak of a bottom, yet housing remains very expensive by any sensible vectors of value (here in the UK at least).

Worst of all, brokers shout BARGAIN BUY STOCKS from proverbial rooftops, yet reported earnings make them look expensive.

There is no doubt that the cash raining down in torrents from magical helicopters is having an effect; but where next?

The SP500 is rolling over and getting a bit of a shellacking today in particular. A simple profit taking retracement, or an end to a dead cat bounce? Will Armageddon part 2 start up after this intermission, or is it the next great bull run.

Doomberg reports that insiders are selling shares at the fastest pace in two years and the put/call ratio is signalling *sell*.

Look, all I want is to put on a nice delta neutral strategy with a nice wide profit zone and go and watch the tennis, supping Champagne, slurping strawberries and cream and watch Andy Murray disappoint the Brits again, as is the tradition. Alas, this market is making me nervous. I have no fear of adjusting, but being full of booze and around the corner at Wimbledon stadium, my mind wandering to fantasy as I watch the ladies play... or not, as the case may be, is just not conducive to high falutin option trading.

So I guess I'll stay home and watch it on TV...I can't get out of my driveway anyway now that The Championships have started anyway. It will have to be pizza and beer, rather than champagne, strawberries and cream.

Here Endeth The Hiatus

I've had an extended break from blogging always promising myself to come back soon. Now is the time. I'm going to have a fiddle with my template and a perhaps a few trivial posts, then into it with some gusto.

Anyone who's followed me for a while will know that I was a bear... vindicated!

I'd like to say that I got rich out of it, alas, as I've also said before, extreme volatility is a bitch to trade. I had some great wins, but also some losses. What's new? Business as usual.

The cool thing is that even through some of the stormiest stock market action for years, option traders can still make a good living, while long only investors were taken to the wood shed. Though the ballsy ones who jumped on at the bottom might be feeling pretty chuffed.

Anyway, for better or for worse, I'm back.

More About Volatility

In the previous article, I received a question with regards to comparing implied volatility (IV) and historical volatility, so I’ll talk a bit about that.

Firstly I want to concentrate on HV. As I’ve pointed out in previous articles, HV looks backwards. A period of time is selected, that is, the most recent x days of data is used to calculate the historical volatility mathematically as per my previous article on volatility.

This begs the question, how many days should we look back over: 10 days, 20 days, 30, 100, 250? The general rule of thumb is either 20 or 30 days, roughly one month. But depending on the look-back period, we can get vastly differing figures for HV.

Consider the following chart where 10, 20, 30 and 100 day HV is plotted: click to enlarge

This shows the vastly differing values that can be derived, depending on the look-back period.

And below, the IV mean compared against 30 day HV for the same chart:

The thing to remember here is that IV is trying to predict future realized volatility. As this chart is of near expiry IVs, it is trying to predict actual volatility about 20 – 30 days ahead, so to truly make a comparison; IV should be compared with HV about a month into the future.

Three things to note here:

1) The market does a reasonably good job of it at times, but drastically wrong at other times.

2) It is not possible to do in real time as we cannot see into the future.

3) Volatility is mean reverting; it tends to oscillate up and down around the mean.

We can use this information to make a “guess” as to what volatility (not direction) will do next. It is suggested in many texts to buy options when IVs are low and to sell options when IVs are high. It is also suggested that options are overpriced when IV is higher than HV, and under priced when IV is lower than HV.

That may be the case at times, but at other times it is absolutely false. It is then clear that assumptions such as these can get you into trouble if applied indiscriminately. But it is a good starting point; just don’t treat it as gospel.

How can the trader tell when options are overpriced or under priced? You can’t! You can only do it in retrospect.

However as traders, we get paid for taking risk. The options trader must make a volatility bet along with a bet on direction (or no direction). So if IVs are high, the question is whether the underlier is about to get very volatile for some reason, or whether option traders have just got a bit carried away and realized volatility does not increase, or falls; and visa-versa.

Implied Volatility

We have now gone through the six inputs into the Black Scholes Option Pricing Model (as proxy for any model in use). The sixth input, volatility, is problematic as a forward guestimation of volatility is used, it is equivocal; different traders will have different ideas of what this input should be.

For instance, I may believe a particular option’s fair value is $2.65 using my own volatility projection, but when I go into the market it may be $3.75, for the sake of example. What is going on?

What is happening here is that the “market” believes that the future volatility of the underlier is going to be a lot more volatile than you do. How does the market do that? Simply by the bids and asks in the market depth and by arbitrage. Depending on your data supplier or broker, there may be a figure supplied called “Implied Volatility”.

This is worked out by algebra, using the first five unequivocal inputs into the option pricing model and the tradable price, which is also unequivocal at that point in time, to derive a volatility figure. So what we are saying here, is that the volatility “implied” by the option’s price is x; Hence “Implied Volatility”.

Let’s look at an example:

* The underlier (XYZ) is trading at 52.75 with no dividend payable.
* I’m looking the XYZ $55.00 call option, which expires in 63 days, which I can buy for $2.45.
* Risk free interest rates are 5%

By plugging those known values into our option pricing model, (in this case I’m using the Cox, Ross & Rubinstein Binomial Model) we can calculate an implied volatility of 36.7%.

So how does that help us?

Quite simply, it is from this figure that you can determine whether the option is fair value or not.

Often in various textbooks and spots around the Internet, the suggestion is to compare Implied Volatility (IV) to Historical Volatility (HV) to determine whether an option is over, or under priced. This is a gross oversimplification. Historical volatility should be studied to get an idea of the volatility characteristics of the underlier, but says very little about what volatility will be going forward.

Remember Implied Volatility looks forward, while Historical Volatility looks backward. For instance, IV can rise before an earnings announcement, sometimes quite dramatically, even though the underlying stock has become very non-volatile as the market waits for the announcement. The market is therefore making a judgment on the volatility once earnings are released. IV invariable drops equally dramatically once the earnings are actually released, as the market discounts the move from the announcement.

The history of Implied Volatility can be plotted on a chart, just like Historical Volatility, again to see the characteristics of IV and how it changes under various circumstances. There are various vendors of IV data, but there is a free source from www. cboe.com from where I sourced the following chart:

The IV plotted in the above is an average of near expiry, implied volatilities across several strikes, so the IV of the particular option you’re interested in may vary somewhat from what is represented here. It does however give the trader an idea of the ebb and flow of volatility over time. You can use this information to make volatility projections and to bet on future volatility fluctuations with a suitable strategy.

The standard wisdom is to buy low volatility and sell high volatility. While this may make sense on the face of it, it isn’t always the wisest thing to do, but more on that later.

Next - More On Volatility

VIX Doldrums

A few thoughts on the situation on the VIX.

From VIX And More:

Dissecting views on VIX technical analysis

VIX Numbers and Overbought Signals

Ten Things Everyone Should Know About the VIX

And from The Daily Options Report:

On VIX @ < 20

Tommorow Cancelled

It certainly has gone a bit quiet and the market seems to be anticipating a repeat of last summer's relentless upward grind.

Sans the end of the world happening, I think that about sizes things up until next earnings season... unless of course the sky does fall down.

Volatility

The sixth and final input into the Option Pricing Model is volatility.

It is my observation that there is often a bit of confusion about this term. If you listen to any of the financial media, volatility is only ever mentioned when the market is going down. To be sure, a 400-point down day on the Dow is a volatile move, but a 400-point up day is never described as volatile, yet it is equally so.

In the simplest terms, volatility is the relative rate at which the price of a security moves up and down. Market technicians have various methods of measuring volatility, using a variety of formulae, but our option pricing model requires a particular measure of volatility; the annualized standard deviation of logarithmic daily change in price.

Now that’s a mouthful, and most option traders view volatility in relative terms without understanding the calculation, but I think it helps to actually understand the mathematics behind it. We can do this with Excel or charting software, which I will give an example of, but let’s do it in English first

We start of by calculating for each day’s data, today’s closing price divided by yesterday’s closing price. This will return a number that is today’s price as a proportion of yesterday’s price. If there is no change, the number will be 1.0, if it is up 2% it will return 1.02, if it is down 5% it will return 0.95 and so on.

The next stage is to find the natural logarithm of the above. This is to reflect the lognormal distribution of stock market returns. Next, multiply this by 100 to express it as a percentage. We can plot this as a scatter chart, which will show the lognormal daily move as a percentage

The next step is to calculate the standard deviation of the above. Normally this is calculated over the last 20 or 30 days of data; it can be any length, but for this example we will use 20 days. This gives us the standard deviation of logarithmic daily change in price, which can be plotted on a chart to see changes in volatility as time goes by. However, Option Pricing Models require that volatility is expressed as an annualized percentage and we do this by multiplying by the square root of the total number of trading days in a year, which is the square root of 252.

This is now the finished volatility calculation, which is called “Historical” or “Statistical” volatility, plotted in the chart below”

This equation can be plotted in charting software to show current and past historical volatility. In Metastock or Amibroker language, (the two platforms I am familiar with) it can be plotted by using the following formula:

(StDev(log(C/Ref(C,-1)),20)*sqrt(252))*100

The above formula calculates historical volatility based on he last 20 days, the figure in red. Any look-back period can be used and some option traders use various length.

So now we can enter this volatility figure into our Option Pricing Model to get an accurate option price; or can we?

The historical volatility number, depending on the look-back period can vary enormously, and as the name implies, looks at past data, whereas what we really want to know as option traders is what volatility will be in the time left until the option expires. As this cannot be known, this forces the option trader to make a volatility forecast, or at least an idea of where volatility might be relative to the present in order to calculate his or her idea of fair value. This where historical volatility can be used as a tool, but the trader must look forward.

Often the market will disagree with you, which I will discuss in the next section.

Next - Implied Volatility