Marginal distribution of some path-dependent stochastic volatility model

A Hobson-Rogers [Hobson, D.G., Rogers, L.C.G. 1998. Complete models with stochastic volatility. Math. Finance 8 (1) 27-48] type “path-dependent” stochastic volatility model is solved explicitly, and the Laplace transform of its marginal distribution is computed in a closed form.