Significantly Lower Estimates of Volatility Arise from the Use of Open-High-Low-Close Price Data

Matthew Modisett and Edgard Maboudou-Tchao

North American Actuarial Journal, 2010, vol. 14, issue 1, 68-85

Abstract: This research provides an indication of the possible reduction in insurance liability valuations arising from the reduced volatility estimate of the Yang-Zhang refinement of volatility, when the liabilities are based on historic prices estimates arising from end-of-day prices in a jump-diffusion model. The paper also demonstrates the usefulness of change points.This research compares the standard measure of volatility (standard deviation of the log of close prices) for the total return of the S&P 500 to a recently developed volatility measure by Yang and Zhang that capitalizes on open-high-low-close prices. The latter volatility was developed to be the measure providing the narrowest confidence interval of all estimates satisfying certain desirable features and as such is the most desirable measure from a decision theory standpoint. This research shows that the Yang-Zhang volatility generally provides significantly lower estimates of volatility. This lower volatility estimate should lead to lower valuation levels for insurance products with guarantees, and this paper provides indicative reductions in liability valuations.Both volatility measures assume constant volatility and drift over a period. To accommodate this assumption, change points are employed to divide historical data into regimes of constant drift and volatility. To this end, the theory of change points is briefly introduced.The research shows that standard measure of volatility generally overestimates volatility, and the error increases with the absolute value of the underlying drift. There are several potential technical reasons why the lower volatility could be invalid, but this paper considers and rejects each, to conclude that the lower volatility estimate of Yang-Zhang is in fact the better estimate, not a result of a technical degeneracy. One conclusion is that valuations employing regime-switching generators, especially insurance liability valuations, should use the Yang-Zhang measure of volatility, otherwise any analysis embedded (or free-standing) options could overvalue prices or volatility. The simplicity of the Yang-Zhang calculation and its potentially large impact on valuations should justify its adoption for most companies.

Date: 2010
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DOI: 10.1080/10920277.2010.10597578

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