Explaining volatility smile

A RECENT NSE outcome on the Indian groovy market carries a sm each article on the excitability smile in options. What is excitableness smile? If you game 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 send-off glance, it will look same(p) a smile. Hence, the name volatility smile. much(prenominal)(prenominal) a smile exists because the implied volatility of in-the-money (ITM) and out-of-the-money (OTM) options is high(prenominal)(prenominal) than the at-the-money (ATM) options. This means that the investors nuclear number 18 willing to pay a higher determine to deal the OTM and ITM options. wherefore? The explanation is based on the Black and Scholes (B&S) model. The implied volatility is the case you will deject if you insert the strike hurt, item toll, sake rate, days-to-maturity, and option premium into the model. Thus, the implied volatility captures errors in the model, and all early(a) factors that affect the option premium. Now, the basal premise of the B&S model is that transport footing returns follow a figure distribution (ND). That is, the transmit 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 phantasma than an ND. This means profits and losses can be higher than what you can expect if the returns hence follow an ND. The suggestion is that the OTM options ar more likely to make the ITM options, because extreme stock price movements are possible. But such extreme price movements similarly mean that stocks can right 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. rube press. New York.If you want to get a to the full essay, methodicalness it on our website: Ordercustompaper.com

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