We introduce the pathwise optimization (PO) method, a new convex optimization procedure to produce upper and lower bounds on the optimal value (the "price") of a high-dimensional optimal stopping problem. The PO method builds on a dual characterization of optimal stopping problems as...

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...

This article develops precise connections among two general approaches to building interest rate models: a general equilibrium approach using a pricing kernel and the Heath, Jarrow, and Morton framework based on specifying forward rate volatilities and the market price of risk. The connections...

An important recent development in the pricing of interest rate derivatives is the emergence of models that incorporate lognormal volatilities for forward Libor or forward swap rates while keeping interest rates stable. These market models have three attractive features: they preclude arbitrage...

This paper describes, analyzes and evaluates an algorithm for estimating portfolio loss probabilities using Monte Carlo simulation. Obtaining accurate estimates of such loss probabilities is essential to calculating value-at-risk, which is a quantile of the loss distribution. The method employs...