Volatility 

Volatility is the measurement of the amount by which the price of the underlying security is expected to fluctuate over a given period of time. Generally speaking, stocks that fluctuate over a wide price range have more volatility. 

Typically, with all other factors being equal, an option’s time value will be higher on a stock with greater volatility. Earthquake insurance will cost more in San Francisco than in Chicago because San Francisco can "move" more.  

For example, take two stocks trading at 100. The 105 May calls on both stocks are $5 out-of-the-money and therefore have no intrinsic value, just time value. The premium for the 105 May calls is at $1 for Stock  A and $2 for Stock B. Even though both options have the same time remaining, Stock B’s calls are trading $1 higher than Stock A’s. This is because Stock B is more volatile. The market is saying that Stock B has a greater chance of moving to 105 than Stock A. Therefore, Stock B demands a higher premium.

Historical Volatility

Historical volatility is a statistical measurement of a stock’s price movements based on history. Typically, it is calculated by taking the standard deviation of the stock’s daily closing price over the past 21 trading days.

Implied Volatility

Implied volatility is the volatility derived from looking at the current market price of an option. Option prices don’t imply a direction of movement for the stock. They only imply a probable distribution or volatility. Increased volatility increases the expected value of an option, but not the expected value of a stock.

Although there are more technical methods of measuring volatility, it is a general rule that if the stock is flat, volatility should be low. If the stock is fluctuating greatly, volatility should be high. The higher the volatility, the higher the risk, and thus option sellers will demand more Option premium. 

The market ultimately determines an options price. The "market" includes market makers, liquidity providers, hedge funds, institutional investors, the public, and even YOU. Remember, the intrinsic or real value of an option will always be constant. The intrinsic value of the 50 call with the stock at 51 will always be $1.00.

However, the options will most likely be trading for more than $1 due to its time value. The time value is determined primarily by the distance the option’s strike price is to the stock price, the stock’s volatility, the current demand for the option,  and the volatility of the stock. 

The more stock can move in price the more money option sellers will want to receive and the more options buyers will have to pay for an option. The marketplace, which factors in all these variables, determines at what price we can buy or sell an option for in the same fashion it establishes stock prices.