Xavier Warin

A regression-based Monte Carlo method to solve backward stochastic differential equations

We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo simulations. A full convergence analysis is derived. Numerical experiments about finance are included, in particular, concerning option pricing with differential interest rates.

Monte-Carlo Valuation of American Options: Facts and New Algorithms to Improve Existing Methods

The aim of this paper is to discuss efficient algorithms for the pricing of American options by two recently proposed Monte-Carlo type methods, namely the Malliavian calculus and the regression based approaches. We explain how both technics can be exploded with improved complexity and efficiency. We also discuss several technics for the estimation of the corresponding hedging strategies. Numerical tests and comparisons, including the quantization approach, are performed.

Valuation of power plants by utility indifference and numerical computation

This paper presents a real option valuation model of a power plant, which accounts for physical constraints and market incompleteness. Switching costs, minimum on-off times, ramp rates, or non-constant heat rates are important characteristics that can lead, if neglected, to overestimated values. The existence of non-hedgeable uncertainties is also a feature of energy markets that can impact assets value. We use the utility indifference approach to define the value of the physical asset. We derive the associated mixed optimal switching-control problem and provide a characterization of its solution by means of a coupled system of reflected Backward Stochastic Differential Equations (BSDE). We relate this system to a system of variational inequalities, and we provide a numerical comparative study by implementing BSDE simulation algorithms, and PDE finite differences schemes.

Gas Storage Hedging

Gas storage hedging based on conditional delta is presented in this paper. Algorithms to calculate hedging strategies are detailed. Some numerical results for fast and seasonal storages show the efficiency of the method compared with finite difference.

Swing Options Valuation: a BSDE with Constrained Jumps Approach

We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method, with respect to the main approximation parameters: the jump intensity

Discrete ordinates methods in xy geometry with spatially varying angular discretization

\lambda

Unbiased Monte Carlo estimate of stochastic differential equations expectations

, the penalization parameter

Numerical approximation of BSDEs using local polynomial drivers and branching processes

p > 0

Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line

and the time step. In particular, we obtain a convergence rate of the error due to penalization of order

Numerical Approximation of a Cash-Constrained Firm Value with Investment Opportunities

(\lambda p)^{\alpha - \frac{1}{2}}, \forall \alpha \in \left(0, \frac{1}{2}\right)