Implied volatility (IV) is not calculated directly using a formula, but rather it is derived by working backward from the market price of an option.
Here's a breakdown of how IV is determined:
Understanding Implied Volatility
- Definition: Implied volatility represents the market's expectation of how much an underlying asset's price will fluctuate over the life of an option. It is a crucial factor in determining option prices.
The Calculation Process
The process of finding implied volatility can be summarized in this table:
| Step | Description |
|---|---|
| 1 | Start with the Option's Market Price: Begin with the current price at which an option is being bought or sold. |
| 2 | Select an Option Pricing Model: Choose a model, like Black-Scholes, that calculates an option's theoretical price. |
| 3 | Input Known Parameters: Input the specific knowns, such as underlying asset price, strike price, time to expiration, interest rates, and dividends into the pricing model. |
| 4 | Iterate to Find IV: The model then is used to calculate the option price, testing different volatility values. The specific volatility that results in the option's theoretical price matching the market price is the implied volatility. This is done iteratively and typically requires numerical methods. |
Key Points:
- Iterative Process: IV is found through trial and error, or more formally, through iterative numerical methods.
- Model Dependent: The calculated IV is dependent on the specific option pricing model used. For example, the implied volatility will likely be different if you use the Black-Scholes model versus a binomial model.
- Not a Prediction: While IV reflects the market's expected volatility, it's not a forecast of actual future volatility.
- Practical Example: If you have an option price of \$5 and all other input parameters in the model, you might try different volatility values until the model yields an option value near \$5, the volatility used to achieve this price is the implied volatility.
Why Use Implied Volatility?
- Option Valuation: It helps in assessing whether an option is overvalued or undervalued relative to current market expectations.
- Trading Strategies: Traders use IV to develop trading strategies, including volatility arbitrage.
- Risk Management: High IV signals higher price fluctuations and thus, higher risk.
Example
To further illustrate, consider that an option is priced at \$2 in the market and you have identified the other parameters for an option pricing model (e.g. Black Scholes). You would then adjust the volatility in the option pricing model until the price produced by the model is as close to \$2 as possible. The volatility number that gets the model to produce \$2 is then the implied volatility.
