Comparison of least squares Monte Carlo methods with applications to energy real options

Abstract

Least squares Monte Carlo (LSM) is a state-of-the-art approximate dynamic programming approach used in financial engineering and real options to value and manage options with early or multiple exercise opportunities. It is also applicable to capacity investment and inventory/production management problems with demand/supply forecast updates arising in operations and hydropowerreservoir management. LSM has two variants, referred to as regress-now/later (LSMN/L), which compute continuation/value function approximations (C/VFAs). We provide novel numerical evidence for the relative performance of these methods applied to energy swing and storage options, two typical real options, using a common price evolution model. LSMN/L estimate C/VFAs that yield equally accurate (near optimal) and precise lower and dual (upper) bounds on the value of these real options. Estimating the LSMN/L C/VFAs and their associated lower bounds takes similar computational effort. In contrast, the estimation of a dual bound using the LSML VFA instead of the LSMN CFA takes seconds rather than minutes or hours. This finding suggests the use of LSML in lieu of LSMN when estimating dual bounds on the value of early or multiple exercise options, as well as of related capacity investment and inventory/production policies.

Optimal expansion timing decisions in multi-stage PPP projects involving dedicated asset and government subsidies

“…and E is a N × N identity matrix. Then, (24) can be expressed as [20], it has been extended to optimal multiple stopping time problems [7,22,23].…”

Pathwise Optimization for Merchant Energy Production

“…Approximating them by sample average approximations is a possibility (Desai et al 2012) but introduces an error in the dual bound estimate. We thus choose basis functions and stochastic models for the evolution of the vector of forward curves that satisfy Assumption 1, which is common in the literature (see, e.g., Nadarajah et al 2017 and references therein) Assumption 1. The expectation E[φ j,b (F j )|F i ] is available in an efficiently computable closed form for each i and j ∈ I \ {I − 1} with j > i and F i ∈ F i .…”

“…The PLP columns that correspond to the coefficients of the basis functions are nearly parallel in our numerical study, which is based on commonly used such functions (see, e.g., Longstaff and Schwartz 2001, Boogert and De Jong 2011, Nadarajah et al 2017, and references therein). That is, the resulting PLP is ill-conditioned and thus difficult to solve.…”

Socially Responsible Merchant Operations: Comparison of Shutdown-averse CVaR and Anticipated Regret Policies

“…The AR and RCVaR SDPs for this instance are both high-dimensional and intractable to solve. We thus use the regress-later least-squares Monte Carlo method [13,7,14] to obtain shutdown-averse policies using AR and RCVaR. We find that the AR policy is more efficient at managing the tradeoff between shutdown probability and asset value compared to RCVaR.…”