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Managing the Complex Risks of Volatility Target Indices and Variable Annuities
By Christian Kahl PhD | January 6, 2016

In mid-November, The Society of Actuaries and Annuity Systems, Inc. held its annual Equity-Based Insurance Guarantees (EBIG) Conference in Chicago. The event provided risk-management and valuation professionals with key information on how to better quantify, monitor and manage the complex risks underlying the variable annuity (VA) and indexed annuity products. FINCAD was in attendance and I presented at the conference.

At this year’s two-day event, a line-up of industry experts talked through several timely topics including: risk metrics used to manage and monitor long-term market risks; the role of risk management and risk management platforms in pricing and hedging, and how to quantify and model policyholder behavior—among others. To kick off the conference, FINCAD held its own welcome reception at Chicago’s iconic restaurant, The Gage.

My presentation was titled: Modeling Variable Annuities and Volatility Control Strategies. In it, I focused on the importance of consistently modeling long-dated investment strategies and, in particular, the embedded interest rate risk inherent to those. Volatility control strategies are becoming ever more popular amongst insurance companies and asset managers as they significantly reduce the capital reserves required, compared to traditional static investment strategies. Moreover, balancing risky and non-risky assets in a dynamic fashion allows firms to generate alpha in both systematically upward and downward trending markets.

Volatility control involves managing assets via the continual rebalancing between a risky asset (oftentimes an equity) and cash. The basic principle here is rather simple in that you have a risky and a non-risky asset, and you measure the volatility of your risky asset and deleverage it when volatility goes up, which is typically the case when markets are going down. Then, you increase the leverage in your risky asset when volatility goes down.

But firms are challenged by pricing volatility target indices because there are so many variations for how a volatility target index could be structured. A few options can include using an exponential volatility estimator compared to equally weighted historical volatility, varying the size of the historical backward-looking or averaging window, taking the maximum of two estimators or linking the strategy to market implied factors such as implied volatility, variance swaps, reference assets or ViX futures.

These challenges are complicated further by the fact that if you use a long-dated volatility target index, you need to worry about stochastic interest rates. The stochasticity of interest rates considerably impacts the volatility of the forward of the underlying process, which is the key component when looking into pricing options on volatility control indices, and particularly long-dated structures. What all this means is that choosing an appropriate hybrid modeling framework when dealing with volatility control indices is crucially important.

In my presentation, I also analyzed volatility control strategies which aim to fix the volatility of the forward rather than the spot. It is in fact possible to create a volatility control strategy agnostic to interest rate volatility.

In most analytics systems, modeling hybrids such as variable annuities require detailed analysis, careful implementation, and only apply to a particular problem. However, a sophisticated valuation and risk analytics solution like FINCAD’s F3 Platform can help you build generic hybrid models with a quasi-analytic approach, affording you major improvements in speed and accuracy. Such a platform solves the problem of capturing stochastic interest rates with the use of numeraire corrections that are computed automatically in an auxiliary simulation prior to the main simulation. In this way, F3 provides a flexible modeling framework that automates much of the detailed analysis that is normally the domain of expert quants.  Furthermore, in F3, the forward price, not the spot price, is modeled as a fundamental variable. This solves many of the challenges around bespoke analysis, and slow performance.

To learn more about modeling long-dated investment strategies and their embedded interest rate risk, please view my technical article: Volatility Control Indices

About the author
Christian Kahl PhD
Christian Kahl PhD
Director, Head of Client Services | FINCAD

Christian is responsible for all client facing quantitative topics and resources globally. In his role, he deals with a wide spectrum of financial industry clients from asset management, hedge funds and insurance companies to accounting firms and sell-side institutions. Additionally, Christian has extensive expertise dealing with regulatory and accounting requirements across all market segments.    

Before joining FINCAD in spring 2015, Christian was the deputy-head of Financial Engineering in the Equity Market and Commodity department of Commerzbank, where he worked for five years supporting various trading desks. Christian Kahl has 10 years experience as a quant in sell-side institutions implementing models in cross asset front office pricing libraries. His quantitative research is largely focused on stochastic volatility modelling and high performance computing.