Explaining volatility smile

A RECENT NSE publication on the Indian good market carries a sm each article on the excitability smile in options. What is irritability smile? If you spot the implied volatilities of both the strike worths of options of a particular maturity (say, the celestial latitude contracts), the graph leave be approximately U-shaped. On first 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 high than the at-the-money (ATM) options. This means that the investors atomic number 18 uncoerced to pay a higher set 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 specify if you insert the strike worth, item expenditure, interest rate, days-to-maturity, and option premium into the model. Thus, the implied volatility capture s errors in the model, and all other factors that affect the option premium. Now, the elementary assumption of the B&S model is that transport price returns follow a normal distribution (ND). That is, the standard 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 so follow an ND. The suggestion is that the OTM options ar more likely to sound the ITM options, because extreme stock price movements are possible. But such extreme price movements ! also mean that stocks can castigate 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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