Simple option pricing models have a few parameters. They are call/put, strike, maturity, interest rate, dividend, and volatility. The dividend is typically assumed based on historical dividend data and consensus from different investment bank research analysts and then confirmed once the company announces. The most subjective parameter is volatility.
To determine volatility, one would look at historical volatility as a reference. For the actual mathematical calculation, I suggest you search the internet.
One key point is which period of historical data to use. Do you consider the past 3 months, 6 months, 1 year, or 2 years? Typically, we need to consider a historical period that is comparable to the option tenor. But just like any past performance of stock price does not imply its future performance. Historical volatility does not imply future volatility.
For most option traders and investors, it is more important to know the implied volatility of options in the exchange-listed options. This is determined by the supply and demand from exchange participants who include market makers, hedge funds, investment bank traders, insurance companies, and individual investors.
The implied volatility of exchange-traded options is typically available from the exchange website. You could also use the option pricing formula to calculate through the "goal seek" approach, ie reverse from using volatility as input to get option price.
Interestingly, many investors when trading options, they do not consider volatility directly. For example, when selling options, individual investors mainly consider the option premium they could collect from selling puts and calls, not focusing on whether the implied volatility of the options are high or low compared to the historical volatility. Market makers consider trading option portfolios to extract profit and they would like to be able to buy options at lower than fair value and sell options at higher than fair value. Fair value is based on market makers' view on option parameters and their most subjective parameter is implied volatility. Option market makers would be keen to pay for options using implied volatility lower than their expected future volatility. Investment Bank traders would pay for options in their structured products at lower volatility than the listed option market. Some hedge fund managers will pay for options to fit their directional view and stop-loss considerations. For example, if the hedge fund manager has set a stop-loss limit of 2% on the S&P 500, the hedge fund manager may spend 2% to buy an out-of-money call option to ensure even if the bet has gone wrong, the fund manager would not exceed the stop-loss limit. Insurance managers may seek protection for their portfolio and buy put options to hedge.
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