TALK BY KNUT SOLNA, UCI
Multiscale Stochastic Volatility Asymptotics
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.