Some simple variance bounds from Stein’s method

Some better bounds on the variance with applications

We derive bounds on the variance of a finite universe. Some related inequalities for the roots of the polynomial equations and bounds for the largest and smallest eigenvalues of a square matrix with real spectrum are obtained.

Steins method, Malliavin calculus and infinite-dimensional Gaussian analysis

This expository paper is a companion of the four one-hour tutorial lectures given in the occasion of the special month Progress in Stein’s Method, held at the University of Singapore in January 2009. We will explain how one can combine Stein’s method with Malliavin calculus, in order to obtain explicit bounds in the normal and Gamma approximation of functionals of in…nite-dimensional Gaussian …...

Simple Variance Swaps

The events of 2008-9 disrupted volatility derivatives markets and caused the singlename variance swap market to dry up completely; it has never recovered. This paper introduces the simple variance swap, a more robust relative of the variance swap that can be priced and hedged even if the underlying asset's price can jump, and constructs SVIX, an index based on simple variance swaps that measure...

Steins lemma, Malliavin calculus, and tail bounds, with application to polymer uctuation exponent

We consider a random variable X satisfying almost-sure conditions involving G := DX; DL X where DX is X’s Malliavin derivative and L 1 is the pseudo-inverse of the generator of the OrnsteinUhlenbeck semigroup. A lower(resp. upper-) bound condition on G is proved to imply a Gaussian-type lower (resp. upper) bound on the tail P [X > z]. Bounds of other natures are also given. A key ingredient is ...

Some Lower Bounds for Estrada Index