Volatility and black scholes

Based on the most helpful WSO content, here's what you need to know about obtaining the volatility value for the Black-Scholes formula:

1. Historical Volatility:

   • This is calculated using past price data of the underlying asset. It measures the standard deviation of the asset's returns over a specific period.

2. Implied Volatility:

   • This is derived from the market price of the option itself. It reflects the market's expectations of the future volatility of the underlying asset. Implied volatility is often used in the Black-Scholes model because it represents the volatility that, when input into the model, gives a theoretical option price equal to the current market price of the option.

Key Points:

• Historical Volatility: Based on past data.
• Implied Volatility: Derived from current market prices and reflects future expectations.

Clarification:

• Implied Volatility is typically used in the Black-Scholes formula because it aligns the theoretical price with the market price of the option.

If you need more detailed explanations or examples, you might want to check out the relevant sections in John C. Hull's "Options, Futures, and Other Derivatives" or other financial modeling resources available on WSO.

Sources: Share the Strangest Interview Questions You've Received, https://www.wallstreetoasis.com/forum/school/options-futures-and-other-derivatives-by-john-c-hull-summary?customgpt=1, Volatility -- good for S&T bonuses?, Q&A: Volatility arbitrage PM, If 100 of us built a model, would any two be the same?