We provide some best-practice recommendations, including the explicit specification of the algorithmic choices and a warning against using off-the-shelf routines. Implied volatility tends to be lowest with ATM options. Thus, we document a previously unknown phenomenon that a portion of the volatility smile is not of an economic nature. The more an option is ITM or OTM, the greater its implied volatility becomes. Despite the successes of the Black-Scholes-Merton model based on Brownian motion and normal distribution, two puzzles which emerged from many empirical investigations, have had much attention recently: 1) the leptokurtic and asymmetric features 2) the volatility smile. Volatility smiles are created by implied volatility changing as the underlying asset moves more ITM or OTM. A trader must be aware of what other factors are driving an option’s price and volatility. More precisely, if the Black-Scholes-Merton model is correct, then the implied volatility should be constant but it is widely recognized that the implied volatility curve resembles a \smile', meaning it is a convex curve of the strike price. While implied volatility is one factor in options pricing, it is not the only factor.A single option’s implied volatility may also follow the volatility smile as it moves more ITM or OTM.Near-term equity options and currency-related options are more likely to have a volatility smile. Not all options will have an implied volatility smile.Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically. Options with the lowest implied volatility have strike prices at the money (ATM) or near the money. The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance.Amongst others, these include the Model based on L vy process 6 such as Merton Jump diffusion model 7, the Kou. However, several models have been proposed to accommodate such properties, particularly the leptokurtic and volatility smile5. The smile shows that the options that are furthest in the money (ITM) or out of the money (OTM) have the highest implied volatility. stock price features such as the leptokurtic and empirical abnormity called volatility smile 4.When options with the same expiration date and the same underlying asset, but with different strike prices, are graphed for implied volatility, the tendency is for that graph to show a smile.
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