# What is the use of implied volatility, the skewness and its surface? [closed]

I am leaning about options, saw various video lectures and read some literature including John C Hull. After a while I forgot where I started and where I am currently and I unable to connect dots. The mathematical equations used in the literature are actually beyond my skill set. But I am trying to understand whats happening. So here is what I started

1) What is a CALL, PUT and the moneyness.

2) BSM - where I could just remember the final formula which is that the price of a Call option is = Underlying price * N(d1) - PV of Strike of the contract * N(d2) and I can only price European options and not American options

3) BSM assumes constant volatility being used in calculation of d1 and d2.

4) Price of a put option + 1 stock of underlying = Price of a call + PV of Strike price to maturity

5) If I look at option chain say on (here), for a single expiry and a constant stock price but varying Strike prices, the volatility has to be implied in BSM to arrive at market price.

6) The implied volatilities against a Strike price has a smile or a skew.

7) Combine 6) with a time to expiration, we can plot a 2d surface in 3dimensions, which we call volatility surface.

Questions

1) What does volatility of an underlying have to do with Strike price of the derivative of the underlying ? Just because both are the components of BSM, do they have to be necessarily related ?

2) The correlation of IV and Strike price tells us that, if the option is deep out of the money or deep in the money, the IV is very high. So lets say there is a call which is deep in the money with a very high IV and very low Strike price, can I assume that the option is demanding a high premium ?

3) What is the fundamental reason behind high IV against a deep out of the money option ? What I read is that if the share price of the underlying decreases that means the company looses capital and it has to burn its cash or borrow it making that company a little riskier to invest. Hence the IV is more for the same.

4) How do I use Vol surface to my benefit as a trader ? When I look at here, then as a trader I will benefit if I am able to arrive at a price which i think is more appropriate, which means I don't want to buy an overpriced option (whether call or put). But if the seller of an option or the buyer both use the BSM models, then I will get the same option chain as what is mentioned in the link, so how can I distinguish ? Are we saying that both the option buyer and seller derive different IVs but if they derive different IVs, then the BSM will give different price.

5) For any events like M&A or declaration of quarterly results of the underlying company, there is a certain excitement in the market, which means people are more inclined towards its derivative, which means as the date nears they sentiment will drive high IVs resulting in high prices of the option but at the same time, time to maturity is reducing day by day, therefore, the price of the option must decrease. Which of these factors have more weight and how can the shape of the vol surface tell me what strategy should I take ?