Strike vs. Volatility

Black & Scholes model assumes that volatility is constant for any strike level and compounded returns of the prices has a normal distribution.

In market practise it is seen that the likelihood of rare events are much greater than that the normal distribution anticipates. Black and Scholes model is used in the market for its robustness and simplicity but is modified to fit the real market conditions.

Black & Scholes model is used to calculate the value of the currency options but the volatility used for each moneyness level for a certain expiry date changes. Since the probability of realizing rare events is greater than the normal distrubtion anticipates, option market demands greater volatility for out of the money options than at the money options. The volatility curve changing with the moneyness of the option is called volatility smile.

Derivative Engines Real Time Option Calculators get the standart quoted volatility data from brokers for several time to expiration periods. When user tries to price an option with any moneyness level with Derivative Engines, real time option calculator generates the volatiltiy for the requested strike and moneyness level with Vanna Volga method.
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