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From the Trading Pits

Trading with Curvature

By From the Trading PitsFOXBusiness

Imagine inheriting $53,000 and deciding to invest the entire amount. You purchase 1,000 shares of Archer-Daniels (NYSE:ADM) for $53 per share. This purchase comes with a very straight-forward risk/reward profile: For every subsequent $1.00 move the stock makes, on paper, it will provide you with a $1,000 gain or loss. That means your ultimate risk is $53,000.

But what if you don’t want to risk your entire interference? There’s another option that gives you the ability to invest in the stock without all the risk of directly buying shares of Archer Daniels.

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You could instead purchase 10 ADM December $53 calls for $1.  This options transaction would give you the right – not the obligation – to buy 1,000 shares of the stock (1 contract equals 100 shares) at $53 before December expiration.  Your ultimate downside risk exposure is the price you paid for the option ($1,000) while your “synthetic” purchase price would be $54,000 ($53.00 strike price + $1.00 premium paid for the option).

Options: Another Tool in Your Kit

Options can be magnificent tools – in the example above, you are spending $1,000 to reserve the right to buy ADM between today and December 20th when the option expires.  If the stock should rally to $75, you will have done well as you have purchased it at $54.00 (recall you must add your purchase price to the strike price).  If the stock should tumble below $53.00 you could either buy the stock at the current price and/or write off your $1,000 call purchase as a good idea gone badly!

The flexibility and leverage of options can and does bequeath layers of complications as options are, by their very nature, sensitive to changes in movement, time, and implied volatility.  Options aren’t hard to comprehend once you grasp they are nothing but contracts priced by the market against the worthy opponent of perceived future unknowable events.  And, that is precisely why options have curvature or convexity as they don’t share the same linear profit and loss characteristics as compared to a stock, bond, or futures contract.

Recall options delta is the speed with which an option moves in price with respect to its underlying asset. The maximum speed is 100% for very deeply in-the-money options, and the minimum speed is 0 for very far out-of-the-money options. For example, SPY (SPDR S&P 500) ref: $207.09 options expiring on 12/05/14.  A $200 call has a 100 delta, thus the call will move 1:1 with the movement of SPY.  The $207 call is at-the-money and will contain a 50 delta, while the $214.00 call will have a 0 delta – expressing that the option won’t change even with movement in SPY.

Continuing with this analogy, the gamma is the acceleration of the option—that is, how fast the option picks up or loses speed (deltas) as the price of the underlying contract rises or falls. Consider the SPY $214 call (0 delta) in the above example.  It is true that the delta is currently 0. However, what needs to happen for the $214 to have a delta?  That is what gamma answers – the stability of your delta. Gamma is expressed as the curvature of an option, or the speed at which the delta of an option changes as the value of the underlying asset changes.  In other words, gamma tells us how much curving there is in a curve.  In professional trading crowds, option gamma is spoken as delta gained or lost per one point change in the underlying asset, with delta increasing by the amount of gamma when the underlying increases, and falling by the same amount of gamma when the underlying decreases.

When gamma is high, delta can begin changing significantly from even a slight move in underlying, implied volatility, or time. Long calls and long puts always have positive gamma. Short calls and short puts always have negative gamma. Stocks or futures are linear and thus have zero gamma because their delta is always 1.

Time or Volatility and its impact on Gamma

Establishing how gamma fluctuates as volatility or time changes largely depends on whether the option is in-the-money, at- the-money, or out-of the-money.  Think of gamma as a hill with the at-the-money strike being the hilltop.  A decrease in volatility (or less time to expiration) makes the hill steeper, concentrating more gamma on the at-the-money strike while much less from the both the in and out-of-the-money strikes.  This should make intuitive sense as lower volatility (or less time to expiration) means less variance or, more surety on where the underlying will land at expiration.

A severe increase in volatility (or more time till expiration) has the opposite effect on gamma where the hill of gamma flattens – taking gamma from the at-the-money strike while distributing more gamma to both the in and out-of-the money strikes.  This should make sense for high volatility or more time till expiry infers more uncertainty to where the underlying will land at expiration.  Other words, it’s easier for the market to judge where a stock will close today than tomorrow, next week, or next month.  Due to this, more gamma (delta instability) is assigned to both in and out-of-the-money strikes compared to lower volatility or less time till expiration.

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