Pricing European-style Asian options based on the arithmetic average, under the Black and Scholes model, involves estimating an integral (a mathematical expectation) for which no easily computable analytical solution is available. Pricing their American-style counterparts, which provide early...

A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by...

In the framework of the displaced-diffusion LIBOR market model, we derive the pathwise adjoint method for the iterative predictor-corrector and one of the Glasserman–Zhao drift approximations in the spot measure. This allows us to compute fast deltas and vegas under these schemes. We compare...

We present an iterative procedure for computing the optimal Bermudan stopping time, hence the Bermudan Snell envelope. The method produces an increasing sequence of approximations of the Snell envelope from below, which coincide with the Snell envelope after finitely many steps. Then, by...

Purpose – The purpose of this paper is to study the importance of business time, and market opening/closing times and days, for American option pricing. Design/methodology/approach – A Bermudan pricing approach is employed whereby the option can be exercised only during the times and days...

We present a new non-nested approach for computing additive upper bounds for callable derivatives using Monte Carlo simulation. It relies on the regression of Greeks computed using adjoint methods. We also show that it is possible to early terminate paths once points of optimal exercise have...

In many of the numerical methods for pricing American options based on the dynamic programming approach, the most computationally intensive part can be formulated as the summation of Gaussians. Though this operation usually requiresO(NN') work when there areN' summations to compute and the...

This paper analyses the robustness of Least-Squares Monte Carlo, a technique proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least-squares regressions in which the explanatory variables are certain polynomial functions. We analyze the impact of...

This paper provides an introduction to Monte Carlo algorithms for pricing American options written on multiple assets, with special emphasis on methods that can be applied in a multi-dimensional setting. Simulated paths can be used to estimate by nonparametric regression the continuation value...

We derive the Green's function for the Black-Scholes partial differential equation with time-varying coefficients and time-dependent boundary conditions. We provide a thorough discussion of its implementation within a pricing algorithm that also accommodates American style options. Greeks can be...