# What is a call/put option, how is it priced, and what is its relation to the volatility of the underlying asset?

### Level 1 - Zero to Options Hero - Options 101

This post is a great place to start if you are just getting into understanding what option contracts are and how professional traders think about them, their impact on overall markets, and profitably trade them.

A call option is a financial contract that gives the holder **the right, but not the obligation, to buy an underlying asset at a specified price within a certain time period**. On the other hand, a put option is a financial contract that gives the holder the right, but not the obligation, to sell an underlying asset at a specified price within a certain time period.

The specified price is known as the **Strike Price** of the option, while the certain time period is the maturity or **Expiration Date** of the option.

For example, if a call option on Tesla (TSLA) stock has a 1-month maturity and a strike price of $300, it means that the call option gives the buyer the right but not the obligation to buy Tesla stock at $300 within a period of 1 month. The expiration date would be 1 month from the time of purchase. For this benefit, the buyer of the option pays an upfront amount, known as the **option premium**, which you can think of as an insurance premium.

The buyer of the option would, all else equal, benefit if Tesla stock became more volatile because the buyer benefits in future scenarios where the price of Tesla is > $300 and does not similarly lose out if the price goes down a lot because the maximum loss is the loss of the premium paid.

There is a lot of fancy math involved in how options are priced (stochastic calculus, partial differential equations, for those interested), but the key takeaway I would say is that **the longer the time to maturity and/or the higher the expected volatility of the underlying asset, the more valuable the option is**. The other major takeaway is that due to the way the Black Scholes model works and its assumptions, the price of an option (its premium) will increase proportionally to the square root of the time to maturity. For example, assuming everything else is constant (same strike price, etc.), an option with 2 months to expiry will be worth ~1.4x (square root of 2) an option on the same underlying with 1 month to expiry,

If you would like to go into more detail, take a look at the Wikipedia page for the Black Scholes model/formula for option pricing.

Another thing that you may hear a lot of when looking at options markets is talk of the implied volatility in the options market. Since the price of options is proportional to the expected volatility of the underlying asset in the future, the prices of options trading in the market can be used to back out what traders call the **implied volatility** of the underlying asset using the Black Scholes model/formula. When prices of options go up as market participants pay higher premiums for them, traders will say that **‘implied volatility is being bid up’ **i.e., the market expects higher volatility of the underlying asset than before.

That’s it for now, appreciate any comments as I roll out the Zero to Options Hero series!

For readers who would like to send us a tip and remain free subscribers for now, we have a tip jar at www.buymeacoffee.com/optionsnerds - Thanks for your support!