Quantitative Insurance Research

The Insurance Research group focus on the application of quantitative models to support insurers meet the financial risk management challenges in their business. Areas of focus include regulatory and economic capital measurement, capital projection, asset liability management and liability valuation.

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.

 

Authors: Aubrey Clayton, Steven Morrison
Date: October 2016

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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.

Author: Steven Morrison, Aubrey Clayton
Date: May 27, 2016
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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).

Author: Steven Morrison
Date: September 17, 2015
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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.

Authors: Steven Morrison, LauraTadrowski
Date: September 17, 2015
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In this paper we consider a framework for evaluating real-world probabilistic forecasts of economic variable, particularly nominal interest rates over quarterly time horizons. The main questions we seek to answer are:

1. How reliably does the model predict the true frequency of observed interest rates?
2. How well does the model distinguish between forecast distributions under changing conditions, e.g., high and low interest volatility?

Authors: Aubrey Clayton, Steven Morrison
Date: June 12, 2015
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Here we consider technical challenges and solutions for internal models to account for dynamic hedging strategies in reducing 1-year VaR capital requirements.

Author: Steven Morrison, Laura Tadrowski
Date: February 18, 2015
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Having calculated an overall capital requirement, insurers are often interested in quantifying how this overall capital can be attributed to sub-portfolios (for example business units, geographical locations or product types) and risk factors. 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.

Authors: Steven Morrison, Laura Tadrowski
Date: August 29, 2014
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The implementation of Least Squares Monte Carlo (LSMC) using multiple polynomial regression for asset-liability 1-year Value-at-Risk has emerged as a leading methodology for Solvency II Internal and Economic Capital models in insurance. And, whilst this approach has consistently provided statistical efficiency and accuracy significantly beyond that obtained from other fitting methods, we continue to research enhancements to this methodology. Such enhancements may be attractive in the context of 1-year VaR and also in new, more demanding applications such as mutli-period capital and hedge projection. This paper discusses what the next generation of advancements in LSMC regression methodology may be, along with their likely relative advantages and disadvantages. This includes consideration of techniques such as neural networks and non-parametric fitting methods.

Authors: Douglas McLean Ph.D, David Redfern Ph.D, Kate Pyper
Date: March 24, 2014
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The risk-based nature of Solvency II creates an opportunity for asset managers to play a more strategic role in insurance asset management — capital-driven investment could be for the insurance industry what liability-driven investment has been for pension funds. In this paper we look at how to measure the illiquidity premiums on offer across the increasingly diverse range of asset classes that a long-term illiquid liability writer such as a fixed annuity business can consider investing in. These risk-adjusted return measures are then used alongside a Solvency II-style capital model to generate capital-driven investment metrics.

Authors: John Hibbert , Craig Turnbull, Gavin Conn
Date: March 24, 2014
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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.

Authors: Aubrey Clayton, Steven Morrison, Craig Turnbull, Naglis Vysniauskas
Date: January 24, 2013
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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.

Authors: Steven Morrison, Laura Tadrwoski
Date: November 27, 2013
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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.

Authors: Aubrey Clayton, Steven Morrison, Craig Turnbull, Naglis Vysniauskas
Date: November 27, 2013
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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 these methodologies to a third application: the multi-year projection of one-year VaR capital requirements. We examine how to fit multi-year liability value functions in the calculation of projected one-year VaR capital requirements, as well as liability valuation.

Authors: Steven Morrison, Craig Turnbull, and Naglis Vysniauskas
Date: November 8, 2013
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In this case study we consider two of the practical challenges faced by insurers in implementing proxy functions: incorporating demographic risk factors and yield curve mapping. We demonstrate the approaches that can be adopted to resolve both issues.

Author: Gavin Conn
Date: October 28, 2013
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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.

Authors: Steven Morrison, Laura Tadrowski
Date: October 4, 2013
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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 a firm's forward solvency projection analytics. This can be extremely useful for firms to project their balance sheets, as well as reserving and capital requirements as part of ORSA and other business planning requirements.

Authors: Steven Morrison, Craig Turnbull, Naglis Vysniauskas
Date: July 17, 2013
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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, together with a case study that illustrates the applications in multi-year stochastic simulations, reverse stress testing, and stress and scenario testing.

Authors: Steven Morrison, Craig Turnbull, and Naglis Vysniauskas
Date: April 1, 2013
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This paper discusses whether the quantitative techniques that have been successfully applied to the nested stochastic challenge arising in 1-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.

Authors: Steven Morrison, Laura Tadrowski, Craig Turnbull
Date: March 1, 2013
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