Explaining volatility smile

A RECENT NSE publication on the Indian keen market carries a sm each article on the irritability smile in options. What is excitability smile? If you plot the implied volatilities of both the strike worths of options of a particular maturity (say, the declination contracts), the graph leave be approximately U-shaped. On start glance, it will look like a smile. Hence, the name volatility smile. such(prenominal)(prenominal) a smile exists because the implied volatility of in-the-money (ITM) and out-of-the-money (OTM) options is higher(prenominal) than the at-the-money (ATM) options. This means that the investors nuclear number 18 automatic to pay a higher legal injury to deal the OTM and ITM options. Why? The explanation is based on the Black and Scholes (B&S) model. The implied volatility is the result you will clear if you commentary the strike legal injury, item outlay, interest rate, days-to-maturity, and option premium into the model. Thus, the implie d volatility captures errors in the model, and all other factors that affect the option premium. Now, the staple fibre assumption of the B&S model is that transport price returns follow a normal distribution (ND). That is, the pullulate price returns form a bell-shaped curve if plotted on a graph. only if this assumption is not true.

The distribution of stock price returns has a fatter tail than an ND. This means profits and losings can be higher than what you can expect if the returns and then follow an ND. The suggestion is that the OTM options ar more likely to move the ITM options, because extreme s tock price movements are possible. But such ! extreme price movements also mean that stocks can turn away sharply, which is why ITM options are also preferred. Naturally, investors will be willing to pay a higher price for these options. And the higher price translates into higher implied volatility. Hence, the volatility smile. Bibliography: Hull, J. 2003. Derivatives. Yahoo press. New York.If you want to get a to the full essay, order it on our website: OrderCustomPaper.com

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