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TALK BY KNUT SOLNA, UCI
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Multiscale Stochastic Volatility Asymptotics
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Knut Solna, UCI ** **

We consider the problem of pricing derivative
securities in an environment of uncertain and changing
market volatility. The popular Black-Scholes model
relates derivative prices to current stock prices through a constant
volatility parameter. The natural extension of this approach
is to model the volatility as a stochastic process.
In a regime with a multiscale or bursty stochastic
volatility we derive an generalized pricing theory
that incorporates the main effects of a stochastic volatility.
We consider high frequency S&P 500 historical pricing data and
analyze these with a view toward identifying important time
scales and systematic features. The data shows a periodic
behavior that depends on both maturity dates and also the trading
hour. We examine the implications of this for modeling and option
pricing.