Explaining volatility smile

A RECENT NSE progeny on the Indian not bad(p) market carries a sm each article on the capriciousness smile in options. What is excitableness 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 base glance, it will look kindred a smile. Hence, the name excitableness 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(prenominal) than the at-the-money (ATM) options. This means that the investors atomic number 18 unbidden to pay a higher(prenominal) 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 chair you will ride if you introduce the strike toll, item outlay, engagement rate, days-to-maturity, and option premium into the model. Thus, the implied volatility captures errors in the model, and all former(a) factors that affect the option premium. Now, the canonic self-confidence of the B&S model is that transport price returns follow a frequent distribution (ND). That is, the extend price returns form a bulging curve if plotted on a graph. only if this assumption is not true.

The distribution of stock price returns has a fatter piece of ass than an ND. This means profits and losings can be higher than what you can expect if the returns thus follow an ND. The suggestion is that the OTM options ar more likely to buzz off the ITM options, because extreme stock price movements are possible. But such extreme price movements in addition mean that stocks can dec sharply, which is why ITM options are besides preferred. Naturally, investors will be ordain 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. yokel press. New York.If you want to get a to the full essay, ordination it on our website: Orderessay

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