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An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on…
This paper studies the equal risk pricing (ERP) framework for the valuation of European financial derivatives. This option pricing approach is consistent with global trading strategies by setting the premium as the value such that the…
Utility based methods provide a very general theoretically consistent approach to pricing and hedging of securities in incomplete financial markets. Solving problems in the utility based framework typically involves dynamic programming,…
We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of the underlying asset. The algorithm computes the prices on recombining binomial trees,…
Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…
Adjoint methods form a class of importance sampling methods that are used to accelerate Monte Carlo (MC) simulations of transport equations. Ideally, adjoint methods allow for zero-variance MC estimators provided that the solution to an…
An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex…
We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the…
We combine the one-dimensional Monte Carlo simulation and the semi-analytical one-dimensional heat potential method to design an efficient technique for pricing barrier options on assets with correlated stochastic volatility. Our approach…
A C++ library for sensitivity analysis of optimisation problems involving ordinary differential equations (ODEs) enabled by automatic differentiation (AD) and SIMD (Single Instruction, Multiple data) vectorization is presented. The discrete…
The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive…
Monte Carlo methods represent a cornerstone of computer science. They allow to sample high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte…
In this paper we present two parallel Monte Carlo based algorithms for pricing multi--dimensional Bermudan/American options. First approach relies on computation of the optimal exercise boundary while the second relies on classification of…
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by…
This study introduces computation of option sensitivities (Greeks) using the Malliavin calculus under the assumption that the underlying asset and interest rate both evolve from a stochastic volatility model and a stochastic interest rate…
This paper introduces a versatile approach for computing the risk of collision specifically tailored for scenarios featuring low relative encounter velocities, but with potential applicability across a wide range of situations. The…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…
Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges for standard numerical methods such as binomial trees or Monte Carlo methods. While the former often scales…
Credit value adjustment (CVA) is the charge applied by financial institutions to the counterparty to cover the risk of losses on a counterpart default event. In this paper we estimate such a premium under the Bates stochastic model (Bates…
We present a fast algorithm for approximate Canonical Correlation Analysis (CCA). Given a pair of tall-and-thin matrices, the proposed algorithm first employs a randomized dimensionality reduction transform to reduce the size of the input…