44 research outputs found
The Heston Riemannian distance function
The Heston model is a popular stock price model with stochastic volatility
that has found numerous applications in practice. In the present paper, we
study the Riemannian distance function associated with the Heston model and
obtain explicit formulas for this function using geometrical and analytical
methods. Geometrical approach is based on the study of the Heston geodesics,
while the analytical approach exploits the links between the Heston distance
function and the sub-Riemannian distance function in the Grushin plane. For the
Grushin plane, we establish an explicit formula for the Legendre-Fenchel
transform of the limiting cumulant generating function and prove a partial
large deviation principle that is true only inside a special set