Senior Director, Insurance Research Group
Dr. Steven Morrison is a senior director in Moody’s Analytics insurance research group. Steven joined Barrie & Hibbert in 2001 and played a leading role in the design and development of B&H's Economic Scenario Generator software. His recent research and advisory work has focused on applications of the Least Squares Monte Carlo (LSMC) proxy modeling technique to multi-period problems, in particular capital projection and projection of dynamic hedge programs in order to assess hedge effectiveness. He pioneered the use of LSMC as a tool for projection of insurance liability values and measurement of economic capital, publishing in industry journals on this topic. He has an MSc in financial mathematics and a PhD in theoretical physics.
An emerging business requirement for North American insurers is the ability to project forward stochastic reserve and capital requirements under various planning scenarios to a specific future date. In this paper we consider applying proxy functions to this task, using function fitting techniques described in our previous research paper Fitting Proxy Functions for Conditional Tail Expectation: Comparison of Methods.
This paper details alternative methods for fitting proxy functions to CTE, employing quantile regression in combination with OLS among other techniques. We compare methods according to quality of fit for an example portfolio of variable annuities.
In this paper, we have considered the use of proxy models as a way of overcoming some of the operational and computational challenges associated with measuring future solvency under different market conditions and ALM assumptions.
This paper provides an introduction to various techniques for efficient calculation of the market-consistent value of a portfolio of insurance policies. Two standard approaches to portfolio valuation are considered: (1) Use of different scenarios through different policies; (2) Portfolio compression through the use of model points. Additionally, the use of proxy functions is introduced as a novel approach to valuation of individual policies.
In this paper, we show a practical application to forecasting capital requirements for real portfolios of participating whole life and annuity business, carried out in a joint research project between Moody's Analytics and New York Life Insurance Company.
The challenge of projecting dynamic hedge portfolios for blocks of Variable Annuities (VA) with complex guarantees has proven to be extremely computationally demanding but also essential for obtaining hedging credit in reserves or capital calculations. Our previous research has argued in favor of proxy function methods such as Least Squares Monte Carlo as alternatives to full nested stochastic calculations, and we have demonstrated the successful application of these methods for hedging in simple option examples including path-dependent options. This paper extends previous work by considering actual VA products with guarantees of the kind offered by insurers in North America and Europe.
Quantitative Insurance Research - The unintended consequences of scenario post-processing in the valuation of insurance liabilities
In this paper we explore the use of scenario re-weighting as a method for post-processing scenario sets to reflect calibration targets without having to recalibrate the model. While post-processing techniques can be quite flexible in their ability to match targets, they may result in unintended changes to distributional assumptions that are not included in the set of calibration targets. Using simple examples, we demonstrate how a scenario set's ability to match a set of vanilla asset prices does not uniquely define the resulting prices of more exotic liabilities (or assets).
In this paper, we discuss the validation of proxy models, commonly used in the insurance industry to replace valuations that would otherwise require Monte Carlo simulation. In practice, proxy model validation inevitably involves a certain amount of subjectivity and is specific to the exact problem at hand. We do not attempt to provide a prescriptive recipe for how validation should be carried out, but rather suggest some general ideas and principles based on our experience implementing proxy models with our clients.
In this paper we consider a framework for evaluating real-world probabilistic forecasts of economic variables, particularly nominal interest rates over quarterly time horizons.
In this note, we consider some of the technical challenges and solutions in adapting internal models to account for the effect of dynamic hedging strategies in
This note describes some of the more popular methods for capital attribution by sub-portfolio, their estimation using Monte Carlo scenarios, and the statistical error in these estimates.
In this paper we extend the analysis contained in a previous case study by considering a more complex example: a lookback option. We show that the methodology can produce a similar quality of fitting performance for the lookback option as in the vanilla option case. We also discuss the methodology adjustments necessary for the Greeks fitting strategy in order to accurately fit to forms of path-dependent, exotic options such as lookbacks.
To obtain recognition for the risk mitigation benefits of hedging in their regulatory capital assessments, variable annuity writers in North America and Europe must perform stochastic projections of the behaviour of their dynamic hedging programs over the lifetime of these long-term liabilities However, the computational difficulties of this calculation result in many firms being either unable to obtain realistic levels of capital relief, or undertaking enormous complex nested stochastic calculations that are expensive, unwieldy and that may involve arbitrary simplifications that undermine confidence in their results. We believe this paper breaks new ground by introducing an entirely different methodology for addressing the highly demanding modeling required in this area, and one which is significantly more efficient, accurate and objective than those applied in industry up until now.
The 1-year Value-at-Risk of the market-consistent balance sheet has emerged as the global industry standard in economic capital assessment in insurance. VaR as a financial risk metric pre-dates the insurance industry's adoption of it, and there has been substantial research and application of techniques for the efficient estimation of tail percentiles which has not yet been adopted by insurers as standard practice. This paper surveys some of those methods and considers how effective they may be in the estimation of the 99.5% 1-year VaR.
A recent research report presented methodologies and case studies for the development of proxy functions for use in efficient multi-year projection of the market-consistent liability values of complex life liabilities. This report further extends the applicability of these methodologies to a third application: the multi-year projection of 1-year VaR capital requirements. We examine how to fit multi-year liability value functions for use in the calculation of projected 1-year Value-at-Risk capital requirements as well as liability valuation.
Over the last five years, target volatility funds – where an asset mix is dynamically re-balanced with the aim of maintaining a stable level of portfolio volatility through time - have emerged as an increasingly popular asset class. In this paper we consider the valuation of guarantees written on target volatility funds, and the sensitivity of these values to the choice of equity model and rebalancing frequency.
In this paper we describe and demonstrate how the capability to efficiently produce robust and accurate proxy functions for CTE(70) run-off reserve behavior across a wide range of multi-timestep, multi-risk-factor scenarios can significantly enhance firms' forward solvency projection analytics. This can be extremely useful for firms to project their balance sheets and reserving and capital requirements as part of ORSA and other business planning requirements.
Insurance groups, motivated by ORSA and wider business planning requirements, are increasingly interested in making medium-term forward projections of their regulatory and economic capital requirements across a range of future economic and business conditions. This paper presents the technical methodologies required to support this type of multi-year projection capability for market-consistent liability valuations, together with a case study that illustrates the applications of this capability in multi-year stochastic simulations, reverse stress testing and stress and scenario testing.
This paper discusses whether the quantitative techniques that have been successfully applied to the nested stochastic challenge arising in one-year VaR in insurance economic capital can also be applied to another nested stochastic problem: that of making a one-year projection of run-off CTE reserve requirements.