Multiscale stochastic volatility asymptotics

Multiscale stochastic volatility asymptotics (2003)

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by Jean-Pierre Fouque , George Papanicolaou , Ronnie Sircar , Knut Solna

Venue:	SIAM J. MULTISCALE MODELING AND SIMULATION
Citations:	18 - 8 self

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Datum	Value	Source
TITLE	Multiscale stochastic volatility asymptotics	INFERENCE
AUTHOR NAME	Jean-Pierre Fouque	user correction
AUTHOR AFFIL		user correction
AUTHOR NAME	George Papanicolaou	user correction
AUTHOR AFFIL		user correction
AUTHOR NAME	Ronnie Sircar	user correction
AUTHOR AFFIL		user correction
AUTHOR NAME	Knut Solna	user correction
ABSTRACT	In this paper we propose to use a combination of regular and singular perturbations to analyze parabolic PDEs that arise in the context of pricing options when the volatility is a stochastic process that varies on several characteristic time scales. The classical Black-Scholes formula gives the price of call options when the underlying is a geometric Brownian motion with a constant volatility. The underlying might be the price of a stock or an index say and a constant volatility corresponds to a fixed standard deviation for the random fluctuations in the returns of the underlying. Modern market phenomena makes it important to analyze the situation when this volatility is not fixed but rather is heterogeneous and varies with time. In previous work, see for instance [5], we considered the situation when the volatility is fast mean reverting. Using a singular perturbation expansion we derived an approximation for option prices. We also provided a calibration method using observed option prices as represented by the so-called term structure of implied volatility. Our analysis of market data, however, shows the need for introducing also a slowly varying factor in the model for the stochastic volatility. The combination of regular and singular perturbations approach that we set forth in this paper deals with this case. The resulting approximation is still independent of the particular details of the volatility model and gives more flexibility in the parametrization of the	user correction
YEAR	2003	INFERENCE
VENUE	SIAM J. MULTISCALE MODELING AND SIMULATION	user correction
VENUE TYPE	JOURNAL	INFERENCE
PAGES	22--42	INFERENCE
TECH	preprint	INFERENCE
CITATIONS	18 found	ParsCit 1.0