A Quick Overview of Options
Options
are financial instruments that
convey the right, but not the obligation, to engage in a future transaction on
some underlying security, or in a futures contract. In other
words, the holder does not have to exercise this right,
unlike a forward or future. In today's markets, it is also
possible to trade volatility directly, through the use of derivative securities such
as options and variance swaps.
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Since the market crash of 1987, it
has been observed that market implied volatility for options
of lower strike prices are typically higher than for higher
strike prices, suggesting that volatility is stochastic,
varying both for time and for the price level of the
underlying security. Stochastic volatility models have been
developed including one developed by S.L. Heston. One
principal advantage of the Heston model is that it can be
solved in closed-form, while other stochastic volatility
models require complex numerical methods
It's common knowledge that types of
assets experience periods of high and low volatility. That
is, during some periods prices go up and down quickly, while
during other times they might not seem to move at all.
Periods when prices fall quickly are often followed by
prices going down even more, or going up by an unusual
amount. Also, a time when prices rise quickly may often be
followed by prices going up even more, or going down by an
unusual amount.
- The vega, which is not a
Greek letter (?, nu is
used instead), measures sensitivity to volatility. The vega
is the derivative of the option value with respect to the
volatility of the underlying,
 .
The term kappa, ?, is sometimes
used instead of vega, as is tau, t, though this is rare.
- Over time volatility always
increases.
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