We study the convergence of Monte Carlo estimators of derivatives when the transition density of the underlying state variables is unknown. Three types of estimators are compared. These are respectively based on Malliavin derivatives, on the covariation with the driving Wiener process, and on...

We present an integral equation approach for the valuation of American-style derivatives when the underlying asset price follows a general diffusion process and the interest rate is stochastic. Our contribution is fourfold. First, we show that the exercise region is determined by a single...

This paper describes a practical algorithm based on Monte Carlo simulation for the pricing of multidimensional American (i.e., continuously exercisable) and Bermudan (i.e., discretely exercisable) options. The method generates both lower and upper bounds for the Bermudan option price and hence...

This paper surveys the literature on option pricing from its origins to the present. An extensive review of valuation methods for European- and American-style claims is provided. Applications to complex securities and numerical methods are surveyed. Emphasis is placed on recent trends and...

Simulation has proved to be a valuable tool for estimating security prices for which simple closed form solutions do not exist. In this paper we present two direct methods, a pathwise method and a likelihood ratio method, for estimating derivatives of security prices using simulation. With the...

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...

We analyze the computational problem of estimating financial risk in a nested simulation. In this approach, an outer simulation is used to generate financial scenarios, and an inner simulation is used to estimate future portfolio values in each scenario. We focus on one risk measure, the...