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...

High-dimensional pricing problems frequently arise with financial options (examples include basket options, outperformance options, interest-rate and foreign currency options) and real options. American versions of these options, i.e., where the owner has the right to exercise early, are...

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 develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to external values of the underlying aset. including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be...

We develop a simulation algorithm for estimating the prices of American-style securities, i.e. securities with opportunities for early exercice. Our algorithm provides both point estimates and error bounds for true security price.

This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be...

This paper develops a method for selecting and analysing stress scenarios for financial risk assessment, with particular emphasis on identifying sensible combinations of stresses to multiple factors. We focus primarily on reverse stress testing - finding the most likely scenarios leading to...