# Mathematics behind Options trading

Mindset for options trading & necessary mathematics!

PROBABILITIES & STATISTICS

- Implied Volatility
- Measuring Implied Volatility
- Probability of Profit
- Standard Deviation
- Strike Price

### Important terms:

**Implied Volatility**

IV is a standardized way to measure the prices of options from stock to stock without having to analyze the actual prices of the options. Implied volatility (we will call it IV) is one of the most important metrics to understand and be aware of when trading options. In simple terms, IV is determined by the current price of option contracts on a particular underlying asset (stock, Index, Forex pair or future). IV is quoted as a “yearly percentage value” that indicates the annualized ** expected one standard deviation range** for the stock (or underlying). For example, an IV of 2.5% on a $200 stock would represent a one standard deviation range of $5 over the year.

What does “**one standard deviation” (**1SD) mean?

One standard deviation covers about 68.2% probability of a stock settling within the expected range as determined by option prices.

In the example of a $200 stock with an IV of 2.5%, it would mean that there is an implied 68% probability that the stock is between $195 and $205 in one year.

**IV expansion**: When the future of an asset becomes more uncertain, there is more demand for insurance on that asset as a result options prices are more expensive as market participants become more uncertain about that stock’s performance in the future. When the uncertainty related to a stock increase and the option prices are traded to higher prices, IV will increase. This is sometimes referred to as an

**IV Contraction**: It is opposite side of IV expansion when the fear and uncertainty related to a stock diminishes. Underlying’s options decrease in price which results in a decrease in IV.