# MODELS FOR OPTIONS PRICING

You may observe, evaluate, and trade options using pricing governed by complex mathematical models. Since these models are already included in the trading systems you use, they are not required to learn. We’ll examine the Black-Scholes model and the Binomial model in this part.

BLACK-SCHOLES MODEL

The Black-Scholes model computes option prices quickly and is the primary source of implied volatility. To solve for IV%, this model needs all other inputs (stock price, expiry, etc.). Contrary to a widespread misperception, implied volatility does not affect option prices; instead, changes in option prices allow us to determine a new value for IV.

Given the complexity of the Black-Scholes model, most trading systems will include IV% figures and, perhaps, predicted move values.

There are six inputs needed to calculate an options price:

- Stock value
- Price per strike
- Expiration date (denoted as a percent of a year)
- The interest rate with no risk
- Dividends
- Consensus volatility (which is the only unobserved variable on this list)
- Here’s a formula for calculating IV using the Black-Scholes model.

**Binary Model**

The binomial model, created in the late 1970s, fits real-time pricing better since it clarifies how implied volatility impacts options. It generates option pricing using a decision-tree architecture and discrete, stepwise price modeling.

The ‘u’ symbol (a move up) and the ‘d’ symbol (a move down) in the formula below represent two potential outcomes that might occur after a binomial tree.

**WHAT IS THE DIFFERENCE BETWEEN IMPLIED VOLATILITY AND REALIZED VOLATILITY?**Volatility traders are interested in what happened and what was anticipated (IV) (realized volatility). We heavily rely on data like implied volatility rank (IVR) to help us make trading decisions because of this.

Compared to historical statistics, actual realized volatility is typically overstated by IV. The excessive dread of uncertainty is the cause, which has the excellent effect of allowing traders to benefit from selling options.

Based on the market’s expectation of movement over a specific period, implied volatility (IV) indicates the current market price for volatility or the fair value of volatility.

Realized volatility is the fluctuation that occurs in an underlying over a predetermined time frame.

**IV may assist with the following:**

- Inform you of the relative cost of alternative prices.
- Assist you in assessing market sentiment or the magnitude of anticipated change.
- Give the marketplace agreement. For instance, the real IV may be directly impacted by the perceived dread of the upside or downside of the IV.
- Give you various opportunities to succeed at expiry or earlier, even if your directional assumption is wrong.

**Using IV won’t assist with the following:**

- Tell you the direction of the stock price
- Identify the movement’s leadership.
- serve as a foolproof stock movement remedy (war, natural disasters, adverse news, etc. influences IV)
- Ensure the success of your approach