In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-dimensional SDEs driven by Brownian motions. Giles has previously shown that if we combine a numerical approximation with strong order of convergence $O(\Delta t)$ with MLMC we can reduce the computational...

In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in the timestep and second...

We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least-squares optimization procedure. With several numerical examples, we show that such Least-squares Importance Sampling (LSIS) provides efficiency gains comparable to the state-of-the-art techniques, for...

A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of...

In this paper, we propose a novel, analytically tractable, one-factor stochastic model for the dynamics of credit default swap (CDS) spreads and their returns, which we refer to as the spread-return mean-reverting (SRMR) model. The SRMR model can be seen as a hybrid of the Black–Karasinski...

We present an accurate and easy-to-compute approximation of zero-coupon bonds and Arrow–Debreu (AD) prices for the Black–Karasinski (BK) model of interest rates or default intensities. Through this procedure, dubbed exponent expansion, AD prices are obtained as a power series in time to...

In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a series expansion of the deviation of its logarithm from...

A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of...

A recently introduced Importance Sampling strategy based on a least squares optimization is applied to the Monte Carlo simulation of Libor Market Models. Such Least Squares Importance Sampling (LSIS) allows the automatic optimization of the sampling distribution within a trial class by means of...

We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least squares optimization procedure. With several numerical examples, we show that such Least Squares Importance Sampling (LSIS) provides efficiency gains comparable to the state of the art techniques, when...