As shares of BP plc (NYSE:BP) attempt a recovery this week from 14-year lows, the prices that investors are paying for insurance in the form of put protection may have peaked, at least temporarily. At the end of trading on Thursday, with BP stock up more than 12% to $32.78, the option premiums for the June 30 puts and the July 30 puts were $1.15 and $2.80 respectively, down from $3 and $5 on Wednesday when the stock dropped dramatically below $30. The June 30 put would protect holders of stock below the $30 level for a cost of $1.15, but only for another week until June options expiration, while the July 30 put offers insurance below $30 all the way to July 16th for its premium of $2.80. Both of these option contracts have seen heavy volume this week as investors and traders scramble for protection and opportunity.

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Above is a Volatility Chart that tells the tale of increased risk in BP stock for the past two months as measured by implied volatility. Implied volatility (IV, for short) is a number that comes from making an option pricing model run backwards, so that instead of putting in an expected or historical volatility to tell you what a fair price for an option should be, you put in the option price currently trading in the market and the model spits out what volatility those options are “implying.” The black line representing the “25 delta puts” is telling you about puts with strike prices below the underlying stock price, for instance, the 35 put when the stock was trading $40 and the 30 put when BP was at $35. Notice the slow rise in May IV as BP’s share price sank, and then the upward spikes in IV in June as the stock slipped below $40 and then fell over $5 in one day to $29 on volume of 240 million shares. Whenever options trade at implied volatilities over 100% it indicates a perception of extreme risk among investors and options traders. Times you may have witnessed this before would be during the financial crisis of 2008 when the CBOE S&P 500 Volatility Index (VIX) (the broad market measure of implied volatility) vaulted above 80% and individual bank stocks had IVs over 200%. Another common example would be biotech stocks whose fortunes hang on the cliff of FDA approvals.

What put prices are telling us about BP’s future

One of the most useful—and easiest—things you can do with implied volatility is to turn it into a daily volatility number so you can see what option markets are expecting for daily price moves in a stock or index. Since volatility is almost always expressed as an annualized number, and since volatility is proportional to the square root of time, the handy option trader’s trick for converting it into a daily number is to divide by 16, the square root of 256 (approximate number of trading days in a year). If you take an implied volatility of 100% and divide by 16%, you get 6.25%. This means that, on average, option markets are pricing in a high probability of 6% daily moves for whatever stock or index has 100% implied volatility. Since we have seen 10% to 15% moves in BP shares on many days in the past few weeks, it should not then surprise you to see implied volatility at levels well above 100%. If we take the highpoint for implied volatility of puts this week, 140%, and convert it into a daily volatility measure we get only 8.75%. One conclusion we might draw is that implied volatility is telling us that option markets don’t expect the stock to go to zero anytime soon. The 30-strike put options that were trading at roughly $3 for the June expiration and $5 for July on Wednesday got cheaper on Thursday for two reasons: First, the rise in BP’s stock price naturally made the price of insurance cheaper as put values almost always fall when a stock rises as much as BP did Thursday. In this case, the $3.58 rise in BP equated to a drop in these put prices between $1.85 and $2.20, which was fairly expected based on their delta probabilities of 0.50 at the time. Delta tells you how much an option is just like the stock and therefore what its probability is of being worth something by expiration. Options with strike prices very close to the underlying stock price will have deltas close to .50, or 50%, and this means that their premiums will move about 50 cents for every dollar the stock moves because they have a 50% probability of being just like the stock. The second reason these put options fell in price is because their “risk premium” dropped, as measured by implied volatility. You can see on the volatility chart that IV fell by over 20 percentage points in one day from Wednesday to Thursday on BP’s rally. That will likely continue as long as two things happen: (1) the oil disaster news front doesn’t worsen (unlikely), and (2) BP stock goes higher, or at least not lower. As BP opens this morning about 75 cents higher, the IV of the July 30 puts has slipped from 105 to 100 already. But 100 is still a hair trigger volatility that should keep investors on the watch.

What’s got shareholders panicked in this black swan event?

Before you rush out and buy BP stock or sell your put protection on this rough analysis of whether the company’s stock goes to $3, or zero, let’s review many of the important risks still facing the company in this crisis: • Washington Political Risk: As President Obama casts threats toward a British sovereign entity about clean-up cost, dividend cuts, and paying for all lost oil worker wages and lost Gulf business revenues, the public relations battle for both BP and Washington have just begun. This is not an environment of certainty upon which BP stock will stage any meaningful recovery, anytime soon. • Spill Estimate Risk: As scientists keep revising their leak projections higher—40,000 barrels per day was the latest revision—the reality of this “black swan” for the big three “E's”—the environment, the economy, and the energy industry—maintains its unpredictable nature. The only thing we know for sure is that we have no idea how dramatically this black swan will impact the “three E’s” a decade from now. As I said on CNBC this morning when asked about BP’s dividend, the long-term impact is the real story. • Costs Escalating Risk: When some investment firm spoke a few weeks ago about this disaster possibly costing BP $40 billion, everyone laughed. No one is laughing anymore. • Plumes Surfacing Risk: More “unknown unknowns” are surfacing in this black swan. Though BP says “there are no known plumes” of oil (essential giant globules floating under the surface), the Gulf ocean is a big place and as with any large and complex problem, you don’t discount the worst, you plan for it.

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