We propose a method for pricing high-dimensional American options on an irregular grid; the method involves using quadratic functions to approximate the local effect of the Black-Scholes operator.Once such an approximation is known, one can solve the pricing problem by time stepping in an...

We propose and test a new method for pricing American options in a high-dimensional setting.The method is centred around the approximation of the associated complementarity problem on an irregular grid.We approximate the partial differential operator on this grid by appealing to the SDE...

Markov chain theory is proving to be a powerful approach to bootstrap highly nonlinear time series. In this work we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular the choice of memory lags and the aggregation of...

We propose a discrete time probabilistic model of depositor behavior which takes into account the information flow among depositors. In each time period each depositors' current state is determined in a stochastic way, based on its previous state, the state of other connected depositors and the...

We propose a discrete time probabilistic model of depositor behavior which takes into account the information flow among depositors. In each time period each depositors' current state is determined in a stochastic way, based on its previous state, the state of other connected depositors and the...

 <font size="1">While the large portion of the literature on Markov chain (possibly of orderhigher than one) bootstrap methods has focused on the correct estimation ofthe transition probabilities, little or no attention has been devoted to theproblem of estimating the dimension of the transition probability...</font>

We extend the short rate model of Vasicek (1977) to include jumps in the local mean. Conditions ensuring existence of a unique equivalent martingale measure are given, implying that the model is arbitrage-free and complete. We develop efficient numerical methods for computation of zero coupon...

Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting. Estimating the Tail Value-at-Risk for large portfolios or pricing basket...