Sequential Design for Optimal Stopping Problems

We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the stopping strategy. Namely, we introduce adaptive generation of the stochastic grids anchoring the simulated sample paths of the underlying state process. This allows for active learning of the classifiers partitioning the state space into the continuation and stopping regions. To this end, we examine sequential design schemes that adaptively place new design points close to the stopping boundaries. We then discuss dynamic regression algorithms that can implement such recursive estimation and local refinement of the classifiers. The new algorithm is illustrated with a variety of numerical experiments, showing that an order of magnitude savings in terms of design size can be achieved. We also compare with existing benchmarks in the context of pricing multi-dimensional Bermudan options.Comment: 24 page

Pricing Interest Rate Exotics in Multi-Factor Gaussian Interest Rate Models

For many interest rate exotic options, for example options on the slope of the yield curve or American featured options, a one factor assumption for term structure evolution is inappropriate. These options derive their value from changes in the slope or cuvature of the yield curve and hence are more realistically priced with multiple factor models. However, efficient construction of short rate trees becomes computationally intractable as we increase the number of factors and in particular as we move to non-Markovian models. In this paper we describe a general framework for pricing a wide range of interest rate exotic options under a very general family of multi-factor Gaussian interest rate models. Our framework is based on a computationally efficient implementation of Monte Carlo integration utilising analytical approximations as control variates. These techniques extend the analysis of Clewlow, Pang and Strickland [1997] for pricing interest rate caps and swaptions.

Analysis of market incentives on power system planning and operations in liberalised electricity markets

The design of liberalised electricity markets (e.g., the energy, capacity and ancillary service markets) is a topic of much debate, regarding their ability to trigger adequate investment in generation capacities and to incentivize flexible power system operation. Long-term generation investment (LTGI) models have been widely used as a decision-support tool for generation investments and design of energy policy. Of particular interest is quantification of uncertainty in model outputs (e.g., generation projections or system reliability) given a particular market design while accounting for uncertainties in input data as well as the discrepancies between the model and the reality. Unfortunately, the standard Monte Carlo based techniques for uncertainty quantification require a very large number of model runs which may be impractical to achieve for a complex LTGI model. In order to enable efficient and fully systematic analysis, it is therefore necessary to create an emulator of the full model, which may be evaluated quickly for any input and which quantifies uncertainty in the output of the full model at inputs where it has not been run. The case study shows results from the Great Britain power system exemplar which is representative of LTGI models used in real policy processes. In particular, it demonstrates the application of Bayesian emulation to a complex LTGI model that requires a formal calibration, uncertainty analysis, and sensitivity analysis. In power systems with large amounts of variable generation, it is important to provide sufficient incentives for operating reserves as a main source of generation flexibility. In the traditional unit commitment (UC) model, the demand for operating reserves is fixed and inelastic, which does not reflect the marginal value of operating reserves in avoiding the events of load shedding and wind curtailment. Besides, the system-wide reserve constraint assumes that the operating reserve can be delivered to any location freely, which is not true in real-world power system operations. To recognize the value and deliverability of operating reserves, dynamic zonal operating reserve demand curves are introduced to an enhanced deterministic UC model for co-optimizing the day-ahead schedules for energy and operating reserves. In the case study on the RTS-73 test system, comparisons are made between the choices of reserve policies (e.g., single, seasonal or dynamic zones) and of different reserve zonal partitioning methods. Results suggest that the enhanced deterministic UC model produces on average lower operational cost, higher system reliability and higher energy and reserve revenues than the traditional one. Finally, we discuss future directions of methodological research arising from current energy system challenges and the computer models developed for better understanding of the impacts of market incentives on power system planning and operations

Bayesian Forecasting in Economics and Finance: A Modern Review

The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be quantified explicitly, and factored into the forecast distribution via the process of integration or averaging. Allied with the elegance of the method, Bayesian forecasting is now underpinned by the burgeoning field of Bayesian computation, which enables Bayesian forecasts to be produced for virtually any problem, no matter how large, or complex. The current state of play in Bayesian forecasting in economics and finance is the subject of this review. The aim is to provide the reader with an overview of modern approaches to the field, set in some historical context; and with sufficient computational detail given to assist the reader with implementation.Comment: The paper is now published online at: https://doi.org/10.1016/j.ijforecast.2023.05.00