Glossary
Asian Option - An Asian-style option has an exercise price equal to the average price of the
underlying asset over a given period. For more information about Asian-style
options, refer to the @EXOTICS XL documentation.
At-The-Money - Refers to an option that would lead to a zero cash flow if the option were to
be exercised immediately.
Bermuda Option - A Bermudan option is an option where early exercise is restricted to certain
dates during the life of the option. It derives its name from the fact that its
exercise characteristics are somewhere between those of the American
(exercisable at any time during the life of the option) and the European (exercisable
only at the expiration of the option) style of options (The island of Bermuda
lies between America and Europe). In addition to an expiration date, Bermudan
options have an "early exercise" date. Before the early exercise date, the option
behaves like a European-style option in that it cannot be exercised. After the
"early exercise" date, the option behaves like an American-style option,
exercisable at any time up until expiration. A common example of this type of
option is an employee stock option where the option holder must possess the option
for a certain period (the vesting period) before the option can be exercised.
Beta Factor - A measurement of how a stock's price varies relative to a broad market index.
The beta factor measures systematic risk while the standard deviation of
historical option prices measures total risk. The beta factor can be seriously
misleading if used in option evaluation models because it measures relative
volatility instead of absolute volatility.
Call Option - An option which gives the holder (buyer of the option) the right to buy the
underlying asset from the writer (seller of the option) at a specific price
within a specified period.
Delta - The rate of change in the price of the derivative security with respect to the
price of the underlying asset. It measures the sensitivity of an option's
price to price changes of the underlying asset. For example, a delta of .5 for an
option on an equity security would suggest that the price of the option would
increase by .50 for every 1.00 that the price of the equity security increases.
Delta (100s) - Simply the delta value times 100.
European Option - A European-style option is an option that may be exercised only at the
option's expiration date.
Exercise Price - The price at which the underlying assets in an option contract will be traded
if the option is exercised. In other words, the price the call option holder
will pay for the underlying security if the option is exercised or the price the
put option holder will sell the underlying asset for if the option is
exercised. Also called the strike price.
Expiration Date - The last date an option contract may be exercised.
Factors Affecting Option Prices
- 1. The current stock price.
Gamma - Gamma measures the sensitivity of the derivative's delta with respect to price
changes of the underlying asset. In simple terms, it measures how quickly the
delta of a derivative will change as the price of the underlying asset
changes. In mathematical terms, it is the second derivative of the change in option
price with respect to price changes of the underlying asset.
Gamma (3.01) - Gamma (3.01) measures the change of an option's delta given a 1.0% change in the price of the underlying asset. Contrast this definition with
that for Gamma which measures the change of an option's delta given a 1 unit
change in the price of the underlying asset. Gamma (3.01) may be more useful than
Gamma in situations where a 1 unit move for the underlying asset would not be
very realistic (i.e., if the price of the underlying asset is very large or
very small). Note that Gamma and Gamma (3.01) would be equal if the price of the
underlying asset is 100, as 1% of 100 would equal 1 unit.
Hedger - Someone who is interested in reducing or eliminating an exposure to a risk
that they already face.
Implied Strike - A value that represents the strike price that would make the market price of
the option the theoretical market price when the historical volatility of the
underlying asset is used as a function input. It represents a way of measuring
an options premium.
Implied Volatility - The value of the volatility variable that is implied or built into the market
option price. It is often referred to as the "market's opinion" of volatility
for the holding period of the option. It represents the "objective" means of
measuring an option's premium.
In-The-Money - Refers to an option that would result in a positive cash flow if the option
were exercised immediately. In the absence of transaction costs, an In-The-Money
option would always be exercised.
Intrinsic Value - The intrinsic value of an option is the maximum of two values, zero and the
value the option would have if it were exercised immediately. The intrinsic
value cannot be less than zero because the option would not be exercised in this
instance. For a call option, the intrinsic value is max (price of the underlying
asset minus the exercise price of the call, 0). For a put option, the
intrinsic value is max (exercise price of the put minus the price of the underlying
asset, 0).
Lambda - The percent change in option value given a one-percent change in the
underlying asset value. Note that the value derived for Lambda from the function is a
percent and not an absolute amount.
Market Option Price - The price, or premium, that is being paid in the open market for the option at
the time of valuation.
Method - Determines the way the cash flows of the underlying asset are to be handled by
the model. The "discrete cash flows" method uses the actual timing of the
dividends for purposes of valuation. This method assumes that the cash flows of an
asset will remain static over the life of the option. The "continuous cash
flows" method calculates a continuous rate based on dividends of the underlying
asset and calculates in the cash flows based on that rate at the end of the
valuation. This method assumes that the cash flows of an asset are dynamic and are in
a constant state of flux or change. The two methods will not usually produces
the same results. Since neither method precisely models the real world, a more
accurate answer is located somewhere in between. For most cases, however, one
method or the other will be sufficient. The most appropriate method depends on
the nature of the underlying asset. For Binomial functions this argument also
determines if the Control Variate technique is used or not.
Model - This function argument refers to either: 1) the actual Model to be used, or 2)
The number of iterations to execute in the binomial method.
Option Class - All options of the same type (either a put or a call) represent an option
class. For example, all put options represent a class.
Option Series - All options of the same class that have the same strike price and the same
expiration date.
Option Styles - The "style" of an option refers to the terms of exercise of the option
(American style, European style, etc.). The "style" of an option determines the time
when the option can be exercised as well as the exercise price. The models in
@OPTIONS XL can handle American-, European- and Bermuda-style options.
Option Type - The "type" of option describes what the option allows the holder to do. A
"put" option allows the purchaser of the option to sell the underlying asset at
the exercise price if the option is exercised. A "call" option allows the
purchaser of the option to purchase the underlying asset at the exercise price if the
option is exercised.
Out-of-the-Money - Refers to an option where a negative cash flow would result if the option were
exercised immediately. It would never be optimal to exercise an
Out-of-the-Money option.
Psi - The sensitivity of an option price to changes in the yield rate.
Put Option - An option which gives the holder (buyer) the right to sell the underlying
asset at a specified price within a specified period. A premium is paid to the
seller or writer of the option.
Repo Rate - The repo rate is the relevant interest rate for many arbitrageurs operating in
the futures market. It is derived from a repurchase agreement where
securities owned by one party are sold to a second party at one price and then
repurchased by the first party after a short period of time at a slightly higher price
(the second party is essentially providing the first party with a loan). The
difference in prices is the interest earned by the second party and the
annualized rate of this amount is called the repo rate. The most common type of repo
rate is the overnight repo rate where the rate is renegotiated every day.
Longer-term agreements called term repos also exist. The repo rate is used for
discounting purposes in the binomial method.
Rho (return value) - The rate of change in the derivative price with respect to changes in the risk
free interest rate.
Rho (function argument) - The coefficient of elasticity.
Risk-Free Interest Rate - The interest rate received from investing in risk-free instruments such as a
U.S. Treasury Bill. See Section 7 of the manual for a complete explanation of
the appropriate type of yield to be used as an input argument for the @OPTIONS
XL function.
Speculator - A trader who wants to take a position in the market.
Strike Price - The price the option holder receives (put) or pays (call) for the underlying
asset if the option is exercised. Also known as Exercise Price.
Strike Sensitivity - The sensitivity of an option price to changes in the strike or exercise price.
Systematic Risk - Risk that cannot be diversified away. It arises from a correlation between
returns from the investment and returns from the stock market as a whole.
Refer to Beta.
Tenor - Refer to Time.
Tenor to Early Exercise - Refer to Time to Early Exercise.
Theoretical Value - The option value generated by a mathematical model given certain prior
assumptions about the terms of the option, the characteristics of the underlying
contract, and prevailing interest rates.
Theta - The rate of change of the value of a derivative with respect to time with all
else remaining the same. It is sometimes referred to as time decay. The theta
derived from the function represents the absolute change in the value of the
option (with respect to time decay) per day.
Theta (7 days) The value of theta derived from the function multiplied by 7.
Time - The actual time from the present, or value date, until the expiration date of
the option.
Time to Early Exercise - The time from the present, or value date, until the time at which the option
can be exercised. For an American-style option, this time is 0 (the option can
always be exercised). For a European-style option, this time is the same as the
basic Time (the option can only be exercised at expiration). For a
Bermuda-style option, this is the amount of time until the "early exercise" date, after
which the option can be exercised at any time. In employee stock option terms (if
early exercise is granted in the Bermuda style, which is by far the most common
case) the tenor to early exercise is the remaining amount of time in the
vesting period (i.e., if the value date is the date the option is granted, the tenor
to early exercise is equivalent to the vesting period).
Underlying - The asset or security from which the derivative security gets it's value. For
an option, it's the asset or security that the holder has the right to buy
(for a call option) or sell (for a put option).
Value Date - The time frame considered to be the "present time" when valuing a stock. In
most cases, the value date is the current date.
Vega - The rate of change of the value of a derivative with respect to the volatility
of the underlying asset.
Volatility - The volatility of a stock price is a measure of uncertainty concerning the
expected future price range of the stock. Volatility is the factor that
differentiates the risk of the asset holder to the risk of the option holder.
Yield Rate - The yield rate is a continuously compounded rate that describes the cash flows
of the underlying asset of an option during the option's life.
2. The strike price.
3. The time of expiration.
4. The volatility of the stock price.
5. The risk-free interest rate.
6. Dividends expected during the life of the option.
Values of rho greater than 1 signify that the variance of the rate of return,
and therefore the standard deviation, increases (decreases) as the price of the
underlying asset increases (decreases).
A value of 1 for rho would correspond to the Black-Scholes process. The
variance of the rate of return would remain constant regardless of the level of the
asset price.
Values of rho less than 1 signify that the variance of the rate of return, and
therefore the standard deviation, decreases (increases) as the price of the
underlying asset increases (decreases).
A value of .5 represents the Square Root Process
A value of 0 represents the Absolute Process.