Stratégies Options - Implied Volatility

I - Option pricing and principles

In theory, in order to price an option, 6 variables and parameters are needed at least ( Black & Scholes : A First Attempt )

2 Variables :
- The spot or underlying
- Time

4 Parameters :
- Strike
- Interest rate (continuously compounded)
- Dividend or revenu rate (continuously compounded)
- Underlying Volatility

II - Option pricing in Reality : a reversed question

In reality option pricing has nothing to do with that way to price an option. Models are used in an inverted manner.
Options are quoted in price, that is, money in euros, in dollars...need to pay or received. But it could be useful to know which volatility number would have been plug into a model to lead a theorical price be equal to a market one.
Traders take the market price and try to figure out which volatility would have to be put in a model in order to match theorical price with market one.

"The crucial concept is about relative cheapness and expensiveness. If an option is widely 'bidded', it would become expensive relatively to others and it's worth to sell what is expensive and to buy what is cheap. What we really trade here is implied volatility " ( in " Le fric " de Jean Manuel Rozan )

Example : A 1 year 100 call is worth $ 14.23 on an option market.
It's known that :
- the underlying asset is worth $100,
- there is no dividend on that given asset,
- 1 year continuously compounded interest rate
Then,
→" it would be needed to plug in a volatility of 30% to make theorical price using Black Scholes pricing model matching market price, say $14.23" The implied Volatility of that particular call is then 30%.

Try our free online implied volatility calculator : here

Nota Bene : Implied volatility is directly linked to a particular model.
Thus, for the same market price, different models would lead to different implied volatilities. Hence, a need for a 'standard' model to be sure every trader will talk about the same thing, using the same language. That standard model is Black & Scholes one.

Black & Scholes model is much more a quoting model than an evaluating one.

A relevant summary,
"Implied volatility is the wrong volatility that one has to plug in the wrong model in order to get the right price".

Download our pricers : here

Next : Volatility Skew or Volatility Surfaces : A First Attempt
Previous: Volatility : Trading Formulae

Related Pdf :
- Modeling and Forecasting Implied Volatility - an Econometric Analysis of the VIX Index
- Pricing Implied Volatility
- Implied Volatility: Statics, Dynamics, and Probabilistic Interpretation

OPTIONS 101 - INDEX
OPTIONS 101 - CHAPTER I
OPTIONS 101 - CHAPTER II
OPTIONS 101 - CHAPTER III
OPTIONS 101 - CHAPTER IV
OPTIONS 101 - CHAPTER V
OPTIONS 101 - CHAPTER VI

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