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Take a look at the current S&P 500 Index (SPX) volatility surface for the extrapolated 1-month (orange) and 3-month (green) option chain below.  In a nutshell, the image gives you a visual depiction of a core violation of the Black-Schole’s model.  The model assumes that the volatility input for all strikes of a given maturity is constant throughout.  This is obviously not the case given that both lines are not perfectly horizontal.  What occurs in the real world is an obvious skew both in a month-to-month and strike-to-strike basis.  This makes volatility hedging a tricky endeavor.  Rather than assuming that volatility is a constant, traders consider them as variables.  As such, volatility is an added risk and subsequently an additional way to make or lose money.  The Black-Schole’s model isn’t perfect, but the fact that everyone uses a modified version of it is testament that it still is the best thing going. For today we are concerned with the strike-by-strike skew within the same month (generic 1- and 3-month expiry).  As you can see below (and is very typical in the equity world), the implied volatilities across all strikes within the same month when graphed looks like a smile.  The…

SPX futures are off 3 points to 2106 as the Shanghai Composite Index has dropped roughly 4%.  This is the biggest drop in three months for China.  Crude oil has surpassed $60 in the US for the first time this year.  The spot VIX finished 12.85 yesterday on the slightly positive day for the SPX.  The VIX futurs are all modestly higher in a steepening of the term structure this morning. Synthetic Straddles–  A VIX term structure in the low teens is historically low, compared to the lifetime mean of roughly 20.  The options market seemingly thinks a move is not forthcoming, at least to the downside.  If everyone believed we were headed lower, the VIX would certainly be quite a bit higher. It seems very well positioned for upward momentum, or in the least not much movement in either direction. You can synthetically create many things with options.  Managers who are long only and believe a major move is coming, one way or the other, can get delta-neutral through the use of SPY at-the-money puts and create a synthetic straddle to take advantage of the impending move.  Being delta-neutral on an at the money call (put), means selling (buying) 500…

S&P futures are up 6 points to 2107.50.  European names are up after the biggest weekly decline this year.  Manufacturing is up in the region more than estimated.  China’s PMI for April is up less than analysts’ estimated.  The cash VIX finished 12.70 on Friday.  The VIX futures are all lower in parallel fashion by a dime on average given the positive tone. Implied Volatility–  Occasionally, I’ll get an email or two that go something like this, “Why should I be so preoccupied with comparing realized stock volatility to that implied in the options if I’m just doing covered calls?”  Let’s take a step back. Definitively, volatility is simply the one standard deviation move in percentage terms of the underlying stock over a one year period.  Given the inputs in the options pricing formula (interest rates, dividends, time to expiration, stock price, strike, and volatility), the volatility is the biggest unknown and the “art” in pricing options.  The volatility input is the means by which one can artificially increase or decrease the price of the option.  That is why most market-makers quote in volatility and remember at what volatility they bought and sold particular months/strikes. Selling covered calls is essentially…

You can glean a lot of information from the put/call parity relationship. Put/call parity (illustrated below) must hold true for names to ensure there is no free lunch arbitrage. The relationship also demonstrates one of the most basic rules of options trading:  puts and calls are interchangeable to a market maker. To a market maker, it makes no difference whether you are long (short) puts or calls on the same strike due to delta hedging. What does matter is the net longs (shorts) on any given strike. As seen below, it is easy to synthetically replicate a put with a call or a call with a put. Call = Put + (Stock – Strike) + PV(Interest on the Strike) – PV(Dividends) Sometimes ,however, the equation gets so out of line you wonder what the heck is going on. In training young market makers, I would often point out that if something is way out of line, assume that you are wrong before jumping in and strapping on a bunch of reversals or conversions. Just as you solved for the call above, you can rearrange the equation (given the market price of the puts and calls) and solve for the dividends…

SPX futures are off 5 points to 2099.75 even against the backdrop of expecations of no rate change by the Fed.  September is generally the expected first date of any increase.  The value of global equities rose to a record $72.2 trillion yesterday (Bloomberg).  Gold is unchanged and crude oil is slightly lower.  The spot VIX finished 13.12 yesterday.  The VIX futures are in a bit of a flattening move with the front months up a bit more than the later months. Option Sensitivity-  In the very least most people associate options trading with gaining exposure (long or short) to a stock/index/etf/etc.  Delta exposure, as it’s called, to the underlying is the most obvious exposure to be sure.  There are, however, many other exposures that complicate things and make options a bit more exciting than simply being long or short a stock.  Volatility trading is another play that I’ve discussed ad nauseum and will not get into here.  But many people don’t realize that you can put on an interest rate or dividend play using options as well. Put-call parity necessitates that options of the same strike and month trade on the same volatility.  If not, an arb can be…