Pricing Models
The Daily Volatility Summary processes end-of-day data using standard
option pricing models. Contracts that permit early exercise (American-style)
are analyzed using the quadratic approximation method. Contracts that must
be held until expiration are priced using the Black-Scholes model.
The pricing inputs for the models are price of the underlying instrument,
days until expiration, strike price, interest rate, and annualized
volatility of the underlying.
Volatility
The values for all the inputs except volatility are easily obtained. To
arrive at a volatility there are two methods employed: implying volatilities
from the price of an option and tracking the actual historical volatility
from the underlying.
Implying Volatilities
Usually the five pricing inputs produce an option price. If you already know
the price of an option, you can imply what the volatility is. A higher
volatility results in more a more expensive option price.
The ATM (at-the-money) volatility is interpolated from the volatilities
of the two strikes that are nearest to the current price of the underlying
instrument.
Historical Volatilities
The historical volatility of the underlying futures is given for a variety
of time periods. All volatilities are annualized.
Standard Deviations
The implied volatilities of ATM option settlements are used to calculate
futures ranges representing one standard deviation. These futures ranges
provide a way to measure and think about time and volatility that
is more concrete and understandable. These statistically expected futures
ranges, in various time periods, are expressed in futures points.
As an example, if the 1-wk standard deviation is 1.52 and the current
futures price is 55.00, then statistically there is a 68.3% chance that
within a seven day time period, the futures will range between 53.48 and
56.52. Two times the standard deviation (3.04 futures points) represents
a 95.4% statistical chance, and three times (5.56 futures points) 99.7%.
ATM, OTM, ITM
Throughout, ATM means at-the-money. Thus, the ATM strike is the strike
nearest the current futures price. OTM refers to the option that is
out-of-the-money. If the current futures price is 63.05 and the 58 strike
is being analyzed, then the 58 put is the out-of-the-money (OTM) option.
Because the 58 call has intrinsic value, it is the in-the-money (ITM) option.
For each strike, a volatility is implied from the settlement price of the
out-of-the-money option. In the case where the futures settle exactly at
the strike, the call and put volatilities are averaged. In addition to
showing the implied volatility of each strike, the Daily Summary calculates
an at-the-money volatility for each contract month. If the DMark futures
settle in between strikes, the "ATM volatility" is interpolated between
the two strikes nearest the futures price. For example, if the futures
settle at a price of 72.20, and if the 72 strike settles at 11 percent
volatility, and the 73 strike settles at 12 percent, then the ATM volatility
would be 11.2 percent. Please note that prices of cabinet are not printed.
It is to be assumed that the only price lower than a single tick is CAB.
Also, all option prices are printed without decimals or dashes separating
the points from the ticks.
Deltas
The delta indicates how much the option price is expected to change
relative to change in the underlying. If an option's delta is .50,
the option price is expected increase 1 tick for every 2 tick increase
in the underlying futures price. Some traders use the at-the-money volatility
to price options at all strikes. The Daily Summary instead uses the implied
volatility to generate option deltas. That is what is meant by
"Implied Delta" -- an option's delta is based on the implied volatility of
that strike. Implied deltas with a "*" indicate that the call delta is
calculated using the put's implied volatility or that the put delta is
calculated using the call's implied volatility. It occurs when there is no
option settlement price available to imply a volatility.
Ticks Over Fair
"Ticks Over" refers to difference between the option's current price
and the price of the option if the ATM volatility were used to generate
an option price. It represents the amount of skew (in ticks) that is
in an option's price.
CR: Conversion/Reversal
CR describes the amount of money (in ticks) that traders demand to carry the
in-the-money option to expiration. As an example, imagine that the March
DMark futures are at 58.50, the 60 put is at 2.41 and the 60 call at .94
Since the put is 1.50 in-the-money, .91 is pure premium (extrinsic value).
A curve that slopes upward indicates
that traders are selling downside options and buying upside options. This
indicates that the market is worried about a huge upside swing. In the case
of markets like the S&P options, the hedge market worries about moves to
the downside. Therefore, hedgers buy downside puts and sell upside calls.
Buying downside puts is like buying insurance. Selling the upside calls is
a way to earn back some of the money that it costs to buy the downside
protection. Some markets, many of them currencies, have no directional bias.
In these cases, there is both a positive upside call skew and a positive
downside put skew. The shape of the curve is like a smile which is why some
traders refer to the skew as the "volatility smile".
Another benefit of the skew is that it generally indicates what will happen
to the at-the-money volatility when the futures swing one way or the other.
If a skew is positive to the upside, that generally indicates that the
at-the-money volatility will be higher when the underlying makes a
significant upside move.
