An option is a derivative.
That is, its value is derived from something else.
In the case of a Index option, its value is based on the underlying Index value.
In the case of a Stock option, its value is based on the underlying Stock value.

Call Option  and Put Option

Call option gives the holder the right, not the obligation, to buy underlying Stock at a fixed price and for a fixed period of time.
A put option gives the holder the right, not the obligation, to sell underlying Stock for a fixed price and for a fixed period of time.
In India Stock Options are American type and  settlement is by cash. Index Options are European type and  settlement is by cash.

The Four Components to an Option

The underlying Stock Value,
The type of option (put or call),
The strike price, and
The expiration date.

At-The-Money, In-The-Money, Out-Of-The-Money

If the stock is trading at a price of 100, the call option at the strike price of 100 is considered to be trading 'at-the-money'.
If the stock is trading above a price of 100, the call option at the strike price of 100 is considered to be trading 'in-the-money'
If the stock is trading below a price of 100, the call option at the strike price of 100 is considered to be trading 'out-of-the-money'

Intrinsic Value

When an option is in-the-money, the price difference between the underlying Stock and the option's strike price is the intrinsic value.

Time Value

Time value is the amount by which the price of the option exceeds its intrinsic value.  The time value premium of an option declines as the expiration date approaches.

Intrinsic Value + Time Value = Option Price

Factors Influencing the Price of an Option

There are four major factors which determine the price of an option. They are:

· The price of the underlying Stock

· The strike price of the option itself

· The time remaining until the option expires

· The volatility of the underlying Stock

Volatility

Historical volatility estimates volatility based on past prices.
Implied volatility starts with the option price as a given and works backward to ascertain the theoretical value of volatility equal to the market price minus any intrinsic value.