Explaining volatility smile

A RECENT NSE publication on the Indian nifty market carries a sm each article on the capriciousness smile in options. What is excitability smile? If you biz 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 starting signal glance, it will look like a smile. Hence, the name volatility smile. such(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 unforced to pay a higher footing 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 render if you stimulation the strike worth, item charge, interest rate, days-to-maturity, and option premium into the model. Thus, the implied volatility captu res errors in the model, and all other factors that affect the option premium. Now, the introductory assumption of the B&S model is that transport price returns follow a normal distribution (ND). That is, the farm animal 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 therefore follow an ND. The suggestion is that the OTM options ar more likely to have the ITM options, because extreme stock price movem ents are possible. But such extreme price mo! vements also mean that stocks can lower 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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