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What is Black–Scholes?
The Black–Scholes model is a mathematical model of a
financial market containing certain derivative investment
instruments. From the model, one can deduce the Black–Scholes
formula, which gives the price of European-style options. lt
is widely used by options market participants. Many
empirical tests have shown the Black-Scholes price is
“fairly close” to the observed prices.
The model was first articulated by Fischer Black and Myron
Scholes in their 1973 paper, “The Pricing of Options and
Corporate Liabilities.” They derived a partial differential
equation, now called the Black–Scholes equation, which
governs the price of the option over time. The key idea
behind the derivation was to perfectly hedge the option by
buying and selling the underlying asset in just the right
way and consequently “eliminate risk". This hedge is called
delta hedging and is the basis of more complicated hedging
strategies such as those engaged in by Wall Street
investment banks. The hedge implies there is only one right
price for the option and is given by the Black–Scholes
formula.
Definition of Options Delta
– options delta is a measure of how sensitive an option
price is to a change in the price of underlying security or
stock. The option delta tells you how much the option price
will change if the price of a stock increases or decreases
by $1 in price. An options delta is the single most
important options Greeks one needs to understand in options
trading.
Definition of Options Gamma
- Options Gamma is defined as the rate of change of options
delta with change of price of the underlying security.
Definition of Options Vega
– Vega is the change in the price of an option from a 1%
change in implied volatility of options. Vega is the single
most important Greek that is ignored by many inexperienced
options traders. Vega is very important and a slight change
in implied volatility results in a very significant change
in price of options. Out of the money options that contain
only extrinsic value, the price is fully determined by Vega
and Theta.
Definition of Options Theta
– Options Theta is defined as measure of rate of change of
time value with the passage of time. It also called time
decay. If everything was held constant, then the option
theta is the loss in price of option per day.
Definition of Rho – Rho
measures the estimated change in the options price with a 1%
change in Interest Rate. Rho is the only Greek that may not
be very important in pricing of options because a 1% in
interest change may only change the price of an option by
about $0.01 which is not very significant. |
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