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EQUITY DERIVATIVES MINI-MASTER
CONTENTS OF THE PAPER:
1) FURTHER EXPLANATION ON VOLATILITY page 2
2) AN EXAMPLE OF CALENDAR SPREAD page 7
3) AN EXAMPLE OF ARBITRAGE SPREAD page 10
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mfilippi@bloomberg.net
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DEFINITION OF VOLATILITY:
Volatility is a measure of the uncertainty of the future price of the underlying asset at the
time when the option expires.
There are three types of volatility: historical, implied and realized. Historical volatility
measures what standard deviation has been experienced over a given historical period;
implied is the value assigned to the volatility in pricing models that equate the modeled
price of an option to the market price of that option; realized volatility is the movement in
the underlying asset between the date when the option is traded and its expiry.
The assumption of the Black-Scholes model is that the volatility of the underlying asset is
constant; therefore the dispersion of asset prices is influenced only by the remaining time
to expiry of the option.
In reality volatility changes over time and for different levels of in-the-moneyness.
PROBLEMS WITH THE ESTIMATION OF HISTORICAL VOLATILITY
There are two alternative estimation processes for obtaining historical volatility: the most
widely utilized method lays on the assumption that volatility is a fixed parameter and that
the historical standard deviation of returns can describe the future probability distribution
of the underlying asset. The second approach considers volatility to be a time-varying
process and uses advanced econometric techniques (i.e. GARCH) to model the volatility
process to be included in the option pricing model.
The calculation of historical volatility raises some important questions:
- how to handle dividends in the volatility calculation? The stock price falls on