M. A. H. Dempster

EVPI‐based importance sampling solution proceduresfor multistage stochastic linear programmeson parallel MIMD architectures

Multistage stochastic linear programming has many practical applications for problemswhose current decisions have to be made under future uncertainty. There are a variety ofmethods for solving the deterministic equivalent forms of these dynamic problems, includingthe simplex and interior‐point methods and nested Benders decomposition, which decomposesthe original problem into a set of smaller linear programming problems and hasrecently been shown to be superior to the alternatives for large problems. The Benderssubproblems can be visualised as being attached to the nodes of a tree which is formed fromthe realisations of the random data process determining the uncertainty in the problem. Thispaper describes a parallel implementation of the nested Benders algorithm which employsa farming technique to parallelize nodal subproblem solutions. Differing structures of thetest problems cause differing levels of speed‐up on a variety of multicomputing platforms:problems with few variables and constraints per node do not gain from this parallelisation.We therefore employ stage aggregation to such problems to improve their parallel solutionefficiency by increasing the size of the nodes and therefore the time spent calculating relativeto the time spent communicating between processors. A parallel version of a sequentialimportance sampling solution algorithm based on local expected value of perfect information(EVPI) is developed which is applicable to extremely large multistage stochastic linearprogrammes which either have too many data paths to solve directly or a continuous distributionof possible realisations. It utilises the parallel nested Benders algorithm and a parallelversion of an algorithm designed to calculate the local EVPI values for the nodes of the treeand achieves near linear speed‐up.

Parallelization and aggregation ofnested Benders decomposition

Dynamic multistage stochastic linear programming has many practical applications forproblems whose current decisions have to be made under future uncertainty. There are avariety of methods for solving these problems including nested Benders decomposition. Inthis method, recently shown to be superior to the alternatives for large problems, the problemis decomposed into a set of smaller linear programming problems. These problems can bevisualised as being attached to the nodes of a tree which is formed from the realizations ofthe random data vectors determining the uncertainty in the problem. The tree is traversedforwards and backwards, with information from the solutions to each nodal linear programmingproblem being passed to its immediate descendants by the formation of their righthand sides and to its immediate ancestor in the form of cuts. Problems in the same timeperiod can be solved independently and it is this inherent parallelism that is exploited inour parallel nested Benders algorithm. A parallel version of the MSLiP nested Benders codehas been developed and tested on various types of MIMD machines. The differing structuresof the test problems cause differing levels of speed-up. Results show that problems withfew variables and constraints per node do not gain from this parallelization. Stage aggregationhas been successfully exploited for such problems to improve their parallel solutionefficiency by increasing the size of the nodes and therefore the time spent calculating relativeto the time spent communicating between processors.

Quantitative fund management

Introduction Part 1: Dynamic Financial Planning Trends in Quantitative Equity Management: Survey Results Portfolio Optimization under the Value-at-Risk (VaR) Constraint Dynamic Consumption and Asset Allocation with Derivative Securities Volatility-Induced Financial Growth Constant Rebalanced Portfolios and Side-Information Improving Performance for Long-Term Investors: Wide Diversification, Leverage, and Overlay Strategies Stochastic Programming for Funding Mortgage Pools Scenario-Generation Methods for an Optimal Public Debt Strategy Solving ALM Problems via Sequential Stochastic Programming Designing Minimum Guaranteed Return Funds Part 2: Portfolio Construction and Risk Management DC Pension Fund Benchmarking with Fixed-Mix Portfolio Optimization Coherent Measures of Risk in Everyday Market Practice Higher Moment Coherent Risk Measures On the Feasibility of Portfolio Optimization under Expected Shortfall Stability Analysis of Portfolio Management with Conditional VaR Stress Testing for VaR and CVaR Stable Distributions in the Black-Litterman Approach to Asset Allocation Ambiguity in Portfolio Selection Mean-Risk Models Using Two Risk Measures: A Multi-Objective Approach Implied Non-Recombining Trees and Calibration for the Volatility Smile

Financial markets. The joy of volatility

Financial markets. The joy of volatility M. A. H. Dempster a; Igor V. Evstigneev b; Klaus Reiner Schenk-Hoppe c a Centre for Financial Research, Statistical Laboratory, University of Cambridge, Cambridge CB5 8AF, UK b Economic Studies, School of Social Sciences, University of Manchester, Manchester, M13 9PL, UK c School of Mathematics and Leeds University Business School, University of Leeds, Leeds, LS2 9JT, UK

Determinants of oil futures prices and convenience yields

Commodity futures prices are usually modelled using affine term structure spot price models with latent factors extracted from the data. However, very little research to date has considered the question – What are the economic drivers behind the calibrated latent factors? This paper addresses this question in the context of a three-factor – short-, medium- and long-term – model for crude oil spot prices by studying the relations between these factors and appropriate economic variables. An affine combination of the short- and medium-term factors is identified as the (instantaneous) convenience yield. Estimating a structural vector auto-regression model we find that the short-term factor mainly relates to demand variables in the physical markets and to trading variables in the futures markets (such as the net short position of commercial hedgers), the medium-term factor relates to business cycles, demand and trading variables, and the long-term factor relates mainly to financial factors.

Developing a Practical Yield Curve Model: An Odyssey

This paper describes the search for a yield curve model that embodies current research but will be used for product pricing, investment advice and asset liability management over long horizons. A variety of available 3-factor affine models are implemented and tested, often with surprising results. The existing model evaluation process leads to a new nonlinear model based on an observation of Black and possessing all the required stylized features for our applications. The examined alternatives all fail in some of these. The efficient implementation developed for the new yield curve model is expected to be the keystone of capital market models in the four major currencies and the paper concludes with some considerations in this direction.

Balanced states in stochastic economies with locally interacting agents

We consider a stochastic model of an economy with locally interacting agents. The structure of interactions among the agents lb described in terms of a directed graph. The arrows of the graph indicate directions of commodity flows in the economic system. We examine states of the system in which material and financial balance constraints are satisfied (balanced states). The constraints under consideration are supposed to hold on a fixed subset of the given graph. The main theme of the work is a comparative analysis of balanced states. Under certain assumptions, we derive exponential estimates for the distances between the balanced states at points lying “deep enough” in the interior of the subset of the graph where the constraints hold.

DC pension fund benchmarking with fixed-mix portfolio optimization

Corporate sponsored defined benefit (DB) pension schemes have recently found themselves in hot water. Accounting practices that led to over-exposure to equity markets, increases in longevity of the scheme participants and low interest rates have all contributed to the majority of schemes in the EU and the UK finding themselves underfunded. In essence, a DB scheme promises to pay its participants an annuity at retirement that gives them a pension equal to a proportion of their final salary (the proportion depending on the number of years of service). Therefore the responsibility to meet these promises (liabilities) rests firmly with the scheme’s trustees and ultimately with the corporate sponsor. The management of these corporate schemes was greatly affected in the past by quarterly earnings reports which directly impacted stock prices in the quest for ‘shareholder value’. Consequently DB scheme sponsors resorted to a management style that was able to keep the liabilities, if not off the balance sheet, then at least to a minimum. One sanctioned tactic that achieved these aims was the ability to discount liabilities by the expected return of the constituent asset classes of the fund. In other words, by holding a large part of the fund in equities, the liabilities could be discounted away at over 10% p.a. The recent performance of the equity markets and the perception of equity as a long-horizon asset class assisted in justifying this asset-mix in the eyes of the scheme’s trustees. However, with the collapse of the equity-market bubble in 2001, many funds found their schemes grossly underfunded and were forced to crystallize their losses by panicked trustees. Consequent tightening of the regulations has made the situation even worse (e.g. all discounting must be done by the much lower AA credit quality bond yield rates in the UK FRS17 standard). As a result many DB schemes have closed and are now being replaced with defined contribution (DC) schemes.y In this world of corporate sponsored DC pension schemes the liability is separated from the sponsor and the market risk is placed on the shoulders of the participants. The scheme is likely to be overseen by an investment consultant and if the scheme invests in funds that perform badly over time a decision may be made by the consultant to move the capital to another fund. However, any losses to the fund will be borne by the participants in the scheme and not by the corporate sponsor. Since at retirement date scheme participants will wish to either purchase an annuity or invest their fund payout in a self-managed portfolio, an obvious need arises in the market place for real return guaranteed schemes which

Latent Jump Diffusion Factor Estimation for Commodity Futures

We introduce a new methodology to estimate the latent factors of a jump diffusion illustrated with an application to the commodity futures term structure. Specifically, we propose a new state space form and then use a modified Kalman filter to estimate models with latent jump-diffusion factors. The method is applied to oil and copper futures prices to pin down long and short term jumps in their futures term structure. Estimates of jump arrival times indicate that both important information surprises and market activities generate jumps of different intensities.

A Practical Robust Long Term Yield Curve Model

This paper describes the initial development and testing of the Black-corrected version of a workhorse 3-factor Gaussian yield curve (term structure) model, the economic factor model (Dempster et al., 2010) which we have used for many years with Monte Carlo scenario simulation for structured derivative valuation, investment modelling and asset liability management with various time steps and currencies. In common with most alternative approaches in the literature to generating non- negative yields using Blacks idea, we propose a simple approximation to the Black mathematical model using the nonlinear unscented Kalman filter. However, its calibration, unlike that of the current computationally intensive alternatives, requires not significantly more computing time than is needed for the linear Kalman filter with the underlying affine shadow rate model. Initial empirical testing of the new Black EFM model both in- and out-of-sample shows acceptable accuracy, sometimes improved over the affine EFM model, which can be improved by UKF tuning in future research. Migration of the system to the cloud can reduce calibration times for both models from a few hours to a few minutes by exploiting massive parallelization of the computationally intensive step.