I am a first year Management & Finance undergrad preparing for my second year Finance courses, given that term 3 and exams have pretty much been cancelled for all British first years.
During that preparation, I am a little bit lost in connecting the dots in option pricing. For option pricing models (binomial, trinomial, Black Scholes) you would need
- Underlying's price
- Strike price
- Current date
- Expiry date
- Dividend yield
Now, what I am stuck with is the volatility and the role of the implied volatility. My problem is that the Black Scholes equation can be used to both calculate the price of an option using the volatility, but also calculate the implied volatility given the option price. How can that work? If I am given the price of an option, it already incorporates the volatility used in the formula. But how would I arrive at the correct option price in the first place when I don't know the implied volatility?
Secondly, I was wondering how exactly options exchanges, say CBOE, arrive at their option prices. If the only information that I am given information is a stock's dividend yield, its entire price history, and the relevant information of an American option like strike price and date of expiry, how would I go about calculating its price? Which volatility would I use?
Thank you very much for your help.