Stock Options Pricing
How do options get their price? This is
a complex subject beyond the scope of what we're doing here, but it is important
to have a basic idea. Market makers use computer models usually based from
'The Black-Scholes' pricing model. This model uses the following inputs to
determine an option price:
-
Stock Price
-
Strike Price
-
Time remaining until expiration
expressed as a percent of a year
-
Current risk-free interest rate
-
Volatility measured standard deviation
To put some perspective on the subject,
let's put the mathematics aside and approach this from a business viewpoint. If
we're a buyer of a call option we have limited risk and the potential for
a large return. If we're the seller we have limited return and the potential for
a large loss. So, if we're the seller what factors would be important to us when
determining the premium we would want to charge for writing this option? Let's
take a look at the factors we would want to consider below:
Volatility:
The more
volatile the underlying security is, the more likely the seller can suffer a
loss. So, the seller protects themselves by charging a higher premium.
Therefore, the higher the volatility increase, the higher the price of the
option.
Time to Expiration:
The longer the time between when the
seller sells the option and the options expirations date, the higher the
probability the seller can suffer a loss. This being the case, the seller will
protect himself. He does this by charging more. Therefore, the longer the option
has before it expires, the higher the price of the option will be.
Sellers Return:
The seller
wants to make a reasonable rate of return on his investment. The more risk he
takes the higher he will expect this return to be. So, the higher the return
expected by the seller, the higher the option price will generally be.
The Greeks:
The
Greeks are a set of statistical values, expressed as percentages that help
determine what options to buy and what strategies to use. We'll use
Delta
and Vega
to help determine which options to purchase, but we'll also provide a brief
definition of some other measurements.
Delta: Delta is a
measure of how the price of an option will move in correspondence to a movement
of the price in the underlying stock. If a call option has a delta of .5
and the stock rises by a dollar the option will rise by .50 [$1 * .5]. The stock
itself has a delta of 1 and an 'in-the-money' option (option with an intrinsic
value) approaches expiration it's delta will approach 1.
In our Microsoft example, let's say the
call option we purchased for 3.10 had a delta of .95 and the stock
increased $2.50. This means the option will rise in price to 5.48 [3.10 +
(2.50*.95)]. If we purchased a put option for $2.10 and this put
had a delta of -.95 and the stock fell by $2.50 -- our out would now be worth
$4.48 [$2.10 + (-2.50*-.95)].
Vega: Another component of determining options price
is the volatility of the underlying security. Vega measures the sensitivity of
option value to change in volatility. Vega indicates an absolute change in
option value for a one percent change in volatility. For example, a Vega of .070
means an option's value will increase by .070 if the volatility percentage is
increased by 1.0, or decreased by .070 if the volatility percentage is decreased
by 1.0.
Theta:
The definition of an option includes a
time constraint. Part of the value of the option is based upon how long it is
before the option will expire. The seller will require greater premium the
longer he must take on the risk. On the buyers side this means that his assets
are depreciating. Theta measures the change in the option value for a one-day
reduction in time to expiration.
Gamma:
Gamma is the sensitivity of Delta in
relation to a movement of the underlying stock. For example, a Gamma change of
0.150 means the delta will increase by 0.150 if the price of the stock increases
or decreases by $1.0.
Rho:
One of the components of determining an
options price is the interest rate. If we're the option seller we would want to
be compensated for taking a risk. The interest rate is one factor that
determines how much compensation we will get. Rho is the sensitivity of option
value to change in interest rate. Rho indicates the change in option value for a
one percent change in the interest rate. For example, a Rho of .05 means the
option's value will increase by .05 if the interest rate is decreased by 1.0.
Open
Interest: Open interest is the number of outstanding
options at each strike price being traded.
We suggest trading stocks that average an absolute minimum
of 250,000 (preferably 500,000) shares traded daily. The reason you want a
minimum of 250,000 daily volume is that there's usually not enough liquidity in
the open interest of the options to make a safe options trade.
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