Analyzing the Bias in the Primal-Dual Upper Bound Method for Early Exercisable Derivatives: Bounds, Estimation and Removal

Joshi, Mark S.

doi:10.2139/ssrn.2415594

Cited by 2 publications

(1 citation statement)

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“…Standard estimates based on the Lipschitz assumption on F can be applied to show that (up to some constants) the variance part decreases as

1 / \sqrt{Λ^{out}}

and the bias part decreases at least like

1 / \sqrt{Λ^{in}}

in the worst case. Recent investigations of Andersen–Broadie‐type algorithms in the optimal stopping case by Belomestny, Dickmann, and Schoenmakers () and Joshi () show that in typical situations, the bias converges as

1 / {normalΛ}^{in}

. Our numerical test examples (in the context of Section below) suggest that beyond the optimal stopping case, the bias may also converge faster than the worst‐case estimates indicate, but a detailed analysis is left to future research.…”

Section: A Primal–dual Algorithm For the Convex Casementioning

confidence: 77%

A Primal–dual Algorithm for Bsdes

Bender

Schweizer

Zhuo

2015

Mathematical Finance

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We generalize the primal-dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dynamic program, which was precomputed, e.g., by least-squares Monte Carlo, this methodology enables us to construct a confidence interval for the unknown true solution of the time-discretized (reflected) BSDE at time 0. We numerically demonstrate the practical applicability of our method in two 5-dimensional nonlinear pricing problems where tight price bounds were previously unavailable.

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“…Standard estimates based on the Lipschitz assumption on F can be applied to show that (up to some constants) the variance part decreases as