The option-pricing model is a mathematical formula, which takes current market factors as inputs then calculates an options theoretical fair market value and associated risk parameters called Greeks.
Spot price: Current market price of the underlying assets or instrument [individual stock].
Strike price: This is the price at which an option permits its owner to buy or sell the underlying asset.
Maturity Date: The date when the option will expire, i.e. it will become worthless after this date. Increasing time to expiration increases the value of calls and puts. The more time remains, the more values the underlier can potentially take on, so the more likely it is for an option to expire in the money.
Interest rate: The interest rate is the current risk-free interest rate.
Increasing interest rate increases the value of a call and decreases the value of a put.
Dividend yield: A financial ratio that shows how much a company pays out in dividends each year relative to its share price. In the absence of any capital gains, the dividend yield is the return on investment for a stock.
Volatility: Volatility is the most interesting price factor to option traders. Volatility is the measure of the speed of the market. Markets that move slowly are low-volatility markets; markets that move quickly are high - volatility markets.
Increasing volatility increases the value of both calls and puts. The more change a stock price, the more likely it is that an option on that stock will expire in the money.
The models output the theoretical price of the option and option risk parameters called "Greeks". The "Greeks" are used to gauge how different movements in the market will affect the price of the option.
Option price: The price (premium) is paid or received for purchasing or selling options.
Increasing stock prices increases the value of a call and decreases the value of a put. A call is an option to buy at a set strike, the more you would have to pay without the call, the better off you are as a holder of the option. A put is an option to sell at a set strike so the relationship is reversed. You want your strike price to be more than you could get by selling spot, so as the stock price increases, the value of a put option decreases.
Increasing strike price deceases the value of a call and increases the value of a put. The difference between spot and strike determines the value of an option, so increasing strike price is like decreasing the stock price and decreasing strike price is like increasing stock price.
Delta: Delta represents the ratio of the change in an option’s price to a given change in the price of the underlying asset or instrument. In other words, if
the underlying changed by a given amount the option price would change by a fraction (the delta) of that amount.
Gamma: Gamma represents the rate of change of an option’s delta with respect to a change in the price of the underlying assets or instrument. In other words,
if the underlying price changed by a given amount the option delta would change by a fraction (the gamma) of that amount.
Rho: Rho represents the rate of change of an option’s price with respect to the change in the risk-free interest rate.
Vega: Vega represents the rate of change of an option’s price with respect to the change in the volatility of the underlying asset or future.
Lambda: Lambda measures the change in option premiums for a percentage point change in its implied volatility. When the lambda value is high, the price of an
option will be more sensitive to small changes in volatility. Conversely, when lambda is low, changes in volatility will have less impact on the options
value.
Theta: Theta represents the rate of change of an option’s price with respect to time. As an option moves closer to expiration the value of Theta increases.