Elena Medova

GLOBAL ASSET LIABILITY MANAGEMENT

Dynamic financial analysis (DFA) is a technique which uses Monte Carlo simulation to investigate the evolution over time of financial models of funds, complex liabilities and entire firms. Although of increasing popularity, the drawback of DFA is the dearth of systematic methods for optimising model parameters for strategic financial planning. This paper introduces strategic DFA which employs the only recently mature technology of dynamic stochastic optimisation to fill this gap. The new approach is described in terms of an illustrative case study of a joint university/industry project to create a decision support system for strategic asset liability management involving global asset classes and defined contribution pension plans. Although the application of the system described in the paper is to fund design and risk management, the approach and techniques described here are much more broadly applicable to strategic financial planning problems; for example, to insurance and reinsurance firms, to risk capital allocation in financial institutions and trading firms and to corporate investment and business development involving real options. As well as describing the mathematical and statistical models used in the case study, the paper treats econometric estimation, asset return and liability scenario generation, model specification and optimisation, system evaluation and historical backtesting. Throughout the system visualisation plays an important role.

Empirical Copulas For Cdo Tranche Pricing Using Relative Entropy

We discuss the general optimization problem of choosing a copula with minimum entropy relative to a specified copula and a computationally intensive procedure to solve its dual. These techniques are applied to constructing an empirical copula for CDO tranche pricing. The empirical copula is chosen to be as close as possible to the industry standard Gaussian copula while ensuring a close fit to market tranche quotes. We find that the empirical copula performs noticeably better than the base correlation approach in pricing non-standard tranches and that the market view of default dependence is influenced by maturity.

Individual asset liability management

A recent discussion of the future of life-cycle saving and investment posed the question: ‘‘Can computer-based personal financial planning models that conform to the principles of economics be both helpful and commercially viable?’’ (Bodie 2007, p. xvii). The heterogeneity of personal financial plans and the interplay between economic considerations and individual aspirations make the problem of personal finance one of the most challenging in economics. At the heart of personal finance problems lies the fundamental consumption/investment problem which has been studied by some of the best minds in economics and finance. Samuelson (1948) devoted much of his early work to communicating the practical implications of economics for household decision making. Modigliani and Brumberg (1954) proposed the life-cycle hypothesis based on the relationship between saving and consumption over a lifetime. Then Samuelson (1969) and Merton (1969) formulated relationships between consumption and portfolio allocation in terms of expected returns and volatilities in order to maximize total lifetime utility. Kahneman and Tversky (1979) introduced a utility function which applies to gains and losses from financial assets and emphasized the qualitative aspects of decisions made by individuals. In spite of the importance of the life-cycle investment and saving problem for the rapidly *Corresponding author. Email: eam28@cam.ac.uk

A framework to measure integrated risk

A framework underlying various models that measure the credit risk of a portfolio is extended in this paper to allow the integration of credit risk with a range of market risks using Monte Carlo simulation. A structural model is proposed that allows interest rates to be stochastic and provides closed-form expressions for the market value of a firms equity and its probability of default. This model is embedded within the integrated framework and the general approach illustrated by measuring the risk of a foreign exchange forward when there is a significant probability of default by the counterparty. For this example moving from a market risk calculation to an integrated risk calculation reduces the expected future value of the instrument by an amount that could not be calculated using the common pre-settlement exposure technique for estimating the credit risk of a derivative.

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.

Risk Profiling Defined Benefit Pension Schemes

A dynamic stochastic optimization model of strategic assetliability management is useful in advising underfunded defined benefit pension schemes on best practice for returning to solvency and long-term stability. The authors present an overview of the dynamic stochastic programming techniques involved and briefly describe the nature of Pioneer Investments proprietary CASM simulator from which the asset class returns and pension scheme liabilities are generated. The stochastic optimization model is described precisely in the article as well as its solution using linear programming. To illustrate the approach, the authors offer two examples of defined benefit schemes using simple, conservative, fund liability models.The optimal dynamic asset allocations of the two examples reflect the motivation of second generation liability-driven investment schemes.Although the final salary scheme models are simple, more complex models can be incorporated with little extra effort into the system described by the authors.Most actuarial assessments used in practice can be modeled for this purpose.

Comparison of Sampling Methods for Dynamic Stochastic Programming

In solving a scenario-based dynamic (multistage) stochastic programme scenario generation plays a critical role, as it forms the input specification to the optimization process. Computational bottlenecks in this process place a limit on the number of scenarios employable in approximating the probability distribution of the paths of the underlying uncertainty. Traditional scenario generation approaches have been to find a sampling method that best approximates the path distribution in terms of some probability metrics such as minimization of moment deviations or Wasserstein distance. Here, we present a Wasserstein-based heuristic for discretization of a continuous state path probability distribution. The chapter compares this heuristic to the existing methods in the literature (Monte Carlo sampling, moment matching, Latin hypercube sampling, scenario reduction, and sequential clustering) in terms of their effectiveness in suppressing sampling error when used to generate the scenario tree of a dynamic stochastic programme. We perform an extensive computational investigation into the impact of scenario generation techniques on the in-sample and out-of-sample stability of a simplified version of a four-period asset–liability management problem employed in practice (Chapter 2, this volume). A series of out-of-sample tests are carried out to evaluate the effect of possible discretization biases. We also attempt to provide a motivation for the popular utilization of left-heavy scenario trees based on the Wasserstein distance criterion. Empirical results show that all methods outperform normal MC sampling. However, when evaluated against each other these methods essentially perform equally well, with second-order moment matching showing only marginal improvements in terms of in-sample decision stability and out-of-sample performance. The out-of-sample results highlight the problem of under-estimation of portfolio risk which results from insufficient samples. This discretization bias induces overly aggressive portfolio balance recommendations which can impair the performance of the model in real-world applications. Thus this issue needs to be carefully addressed in future research, see e.g. Dempster et al. (2010).

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.

Planning for Retirement: Asset Liability Management for Individuals

Pension systems are in crisis. Every day brings dire warnings of future pov-erty across the globe for large numbers of older people. Governments and corporations are pushing the responsibility for pensions and health care back to individuals. With current demographic trends, the present workforce will be faced with the problem of significant ‘pension gaps’ which, unless somehow covered, will force drastic changes in their post-retirement lifestyles. The relatively affluent are no exception. For the last few years, even before the crisis, Fortune magazine has devoted an annual special issue to the problem, with subtitles like ‘Take control of your future’. For example, the July 2006 issue begins: ‘Traditional pensions are melting away…’. By and large, however, the asset management industry remains focussed on asset returns measured by relative performance and treats individuals’ liabilities, at best, in aggregate in terms of asset return goals. Financial planning and wealth management advice for individuals sorely needs innovation.

Portfolio management for pension funds

This paper introduces the use of dynamic stochastic optimisation for pension fund management. The design of such products involves econometric modelling, economic scenario generation, generic methods of solving optimization problems and modelling of required risk tolerances. In nearly all the historical backtests using data over roughly the past decade the system described (with transactions costs taken into account) outperformed the benchmark S&P500.