Saturday, December 7, 2013

Explaining volatility smile

A RECENT NSE publication on the Indian cracking market carries a sm each article on the irritability smile in options. What is irritability smile? If you plan 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 runner 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 nuclear number 18 impulsive 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 reach if you stimulus the strike toll, item hurt, interest rate, days-to-maturity, and option premium into the model. Thus, the implied volatility captures er rors in the model, and all other factors that affect the option premium. Now, the radical assumption of the B&S model is that transport price returns follow a normal distribution (ND). That is, the worsening price returns form a bell-shaped curve if plotted on a graph. only if this assumption is not true.
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The distribution of stock price returns has a fatter tail than an ND. This means profits and losses can be higher than what you can expect if the returns thence follow an ND. The suggestion is that the OTM options ar more likely to turn over the ITM options, because extreme stock price movements are possible. But such extreme price movements a! lso mean that stocks can decline 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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