Maciej Wisniewolski
On some Brownian functionals and their applications to moments in lognormal and Stein stochastic volatility models.
Wed, 02/02/2011 - 16:01 — SomNambulAuthors: Jacek Jakubowski, Maciej Wisniewolski
Subjects: Probability
AbstractThe aim of this paper is to present the new results concerning some
functionals of Brownian motion with drift and present their applications in
financial mathematics. We find a probabilistic representation of the Laplace
transform of special functional of geometric Brownian motion using the squared
Bessel and radial Ornstein-Uhlenbeck processes. Knowing the transition density
functions of the above we obtain computable formulas for certain expectations
of the concerned functional.Probabilistic representations of the density function of the asset price and of vanilla options in linear stochastic volatility models.
Mon, 09/28/2009 - 15:24 — SomNambulAuthors: Jacek Jakubowski, Maciej Wisniewolski
Subjects: Pricing of Securities
AbstractWe derive probabilistic representations for the probability density function
of the arbitrage price of a financial asset and the price of European call and
put options in a linear stochastic volatility model with correlated Brownian
noises. In such models the asset price satisfies a linear SDE with coefficient
of linearity being the volatility process. Examples of such models are
considered, including a log-normal stochastic volatility model. In all examples
a closed formula for the density function is given.
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