Volatility Models: Stochastic volatility
Why are more complex volatility models required? The answer is simple – because the prices from stochastic engines are not supported
by market prices. As a result financial engineers have to recali-brated model parameters every day to the new market data. It is not
consistent with an accurate de-scription of the dynamics. The next (but not the last ) step in the volatility models history is the mod-els
with stochastic volatility.
Numerous pricing models that treat the volatility as a stochastic variable have been proposed over the past decade. The introduction of
a second stochastic process presents new complexity, it is related to the risk-neutral valuation concept. Because we have two sources
of randomness (price and volatility) and the volatility is not a traded asset we must hedge our option with two other contracts, one being
the underlying asset as usual, but now we also need another option to hedge the volatility risk.
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