For evaluating a hedging strategy we have to know at every instant the solution of the Cauchy problem for a parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to find these magnitudes by Monte Carlo simulation of the corresponding system of...

We introduce a new Monte Carlo method for constructing the exercise boundary of an American option in a generalized Black-Scholes framework. Based on a known exercise boundary, it is shown how to price and hedge the American option by Monte Carlo simulation of suitable probabilistic...

In this article we propose several pathwise and finite difference based methods for calculating sensitivities of Bermudan options using regression methods and Monte Carlo simulation. These methods rely on conditional probabilistic representations which allow, in combination with a regression...

The paper focuses on the problem of pricing and hedging a European contingent claim for an incomplete market model, in which evolution of price processes for a saving account and stocks depends on an observable Markov chain. The pricing function is evaluated using the martingale approach. The...

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are: (1) the study is non-asymptotic, that is, the sample size is fixed and does not tend to infinity; (2) the parametric assumption is possibly...