the single vol Black- Scholes model.
Consider this: If the at-the-money (ATM)
IV for a $100 stock is 25%, and you use that
25% to price the options with 60 days to
expiration at the 90 strike, the 90 put would
have a theoretical value of 0.72. But say that
put’s market price is 1.20. That would make
its implied vol 30%. That higher implied vol
is a signal of how likely the market considers
a large potential price change for the stock.
If the market doesn’t anticipate larger price
changes—up or down—the further OTM
options have lower values and lower implied
vols. If the market anticipates larger price
changes, like it might around earnings or a
news event, the further OTM options have
higher values and higher implied vols. Kurtosis is why we see implied vol skew.
In fact, the story goes that implied vol
skew was born during the ’87 crash. Before
that, market makers were cool with pricing
a stock’s or index’s options with a single vol.
Why? Most of those guys weren’t around in
1929, and hadn’t seen the market drop that
much in a single day. Then Black Monday
happened, wiped out a whole bunch of
traders, and taught the survivors about the
potentially higher frequency of large price
drops. Since then, OTM options have had
higher implied vols because traders understand that a crash could happen at any time
and naturally price those options higher.
To see the impact of kurtosis on options
in action, go to the Trade tab on your
thinkorswim® platform by TD Ameritrade
and look at equidistant OTM
calls and puts in the same
expiration (Figure 2). For
example, if the stock is $100,
look at the 90 puts and 110
calls. If you see the 90 puts
trading for 1.10, and the
110 calls trading for 1.00, that suggests the
market anticipates the stock is somewhat
more likely to have a 10-point drop than
a 10-point rally. The market expects the
distribution of returns could have a slightly
fatter tail on the downside.
Alternatively, if the 90 puts were $1.50,
and the 110 calls $1, this suggests the market’s
fear of a $10 drop is higher than the expectation the stock could rise $10. In this case,
the market expects the kurtosis—deviation
from the normal distribution—to potentially
be much larger. The downside tail would be
expected to be fatter than the upside tail.
Just because OTM options are often
priced to reflect what the market anticipates doesn’t mean that bad news always,
or necessarily, happens. On the other hand,
if options prices indicate the market is calm
and no large price changes are expected, just
remember the market often has a mind of its
own. Stay alert. Normal is often a mirage.
So, the expectation of kurtosis in the
distribution of stock returns and indices can
boost the relative theoretical values of OTM
options. And that can help guide your choice
of strategy. As a trader, you might be tempted
to sell those naked options short, believing
this “kurtosis” thing won’t happen to you. If
you make that mistake, you could lose your
entire account value. Look at 2008. That was
a big drop that placed historical market data
miles from a nice, clean normal distribution.
That’s why using defined-risk verticals
when you see higher implied vols (that is,
bigger expected kurtosis) could be a smarter
choice, albeit with a higher commission.
If you’re bullish, for example, and you see
much higher implied vol for O TM puts, a
short put vertical that’s short an OTM put
and long a further OTM put, can still take
advantage of the elevated put prices. But its
defined-risk nature—max risk being the difference between the strikes minus the credit
received—means that even if the market
crashes, the loss, while bad, is not necessarily
KEEP ’EM SMALL
So, you begin to understand that larger,
unforeseen (aka “black swan”) price changes
could wipe you out. But suppose you still
want to sell naked options. Consider selling
further OTM options to give the stock or index more room to drop or rise before it passes the breakeven point of the short options.
Yes, you’ll have a smaller potential profit
selling a further O TM option, regardless of
its implied vol. But that extra amount OTM
could give you some cushion. Remember,
though, it only takes one big price change
to cause catastrophic losses on short naked
options. Keep these positions small and
monitor them closely.
Kurtosis sounds like a scary virus, but
it’s just fancy market geek-speak for something that, at times, could be quite revealing
regarding market data. Don’t worry too
much about theories and formulas and the
numerical kurtosis. Focus on seeing hard
evidence before you put on an options trade,
and adjust your strategy thoughtfully. Your
doc may not give you amazing news, but you
likely have recourse. As always, don’t doubt
FIGURE 2: How skewed are you? Look at OTM puts and calls that are the same distance away from the stock price
to compare the difference in their prices. If the difference is big it’s not a normal distribution. It could be kurtosis
and skew. Source: thinkorswim by TD Ameritrade. For illustrative purposes only.
For more information on the general risks of trading
and trading options, see page 37, #1– 2.
Thomas Preston is not a representative of
TD Ameritrade, Inc. The material, views and opinions expressed in this article are solely those of the
author and may not be reflective of those held by
TD Ameritrade, Inc.
Naked option strategies involve the highest amount
of risk and are only appropriate for traders with the
highest risk tolerance.