Abstract
Contemporary actuarial and accounting practices (APN 110 in the South African context) require the use of market-consistent models for the valuation of embedded investment derivatives. These models have to be calibrated with accurate and up-to-date market data. Arguably, the most important variable in the valuation of embedded equity derivatives is implied volatility. However, accurate long-term volatility estimation is difficult because of a general lack of tradable, liquid medium- and long-term derivative instruments, be they exchange-traded or over the counter. In South Africa, given the relatively short-term nature of the local derivatives market, this is of particular concern. This paper attempts to address this concern by: — providing a comprehensive, critical evaluation of the long-term volatility models most commonly used in practice, encompassing simple historical volatility estimation and econometric, deterministic and stochastic volatility models; and — introducing several fairly recent nonparametric alternative methods for estimating long-term volatility, namely break-even volatility and canonical option valuation. The authors apply these various models and methodologies to South African market data, thus providing practical, long-term volatility estimates under each modelling framework whilst accounting for real-world difficulties and constraints. In so doing, they identify those models and methodologies they consider to be most suited to long-term volatility estimation and propose best estimation practices within each identified area. Thus, while application is restricted to the South African market, the general discussion, as well as the suggestion of best practice, in each of the evaluated modelling areas remains relevant for all long-term volatility estimation. KEYWORDS : Long-term volatility modelling; market-consistent valuation, historical volatility, deterministic volatility models, GARCH, stochastic volatility, break-even volatility, canonical valuation
Highlights
1.1 Since the inception of modern asset pricing models, starting as far back as Bachelier (1900), there has been considerable interest in volatility research
Given the large quantity of life policies written with embedded investment derivatives as well as the current proclivity of many long-term insurers to continue to write similar policies, this should be a material concern for market-consistent valuation
3.1.2 advisory practice notes (APN) 110 suggests the use of historical volatility analysis for estimating the most appropriate long-term volatility parameter to be used in a particular stochastic volatility model in the case where traded derivatives are not available
Summary
1.1 Since the inception of modern asset pricing models, starting as far back as Bachelier (1900), there has been considerable interest in volatility research. 3.1.2 APN 110 suggests the use of historical volatility analysis for estimating the most appropriate long-term volatility parameter to be used in a particular stochastic volatility model in the case where traded derivatives are not available. A better definition of historical volatility would be: the ex-post variation of an asset’s returns taken at a particular frequency over a particular period This succinctly connects the three fundamental variables latent in any volatility calculation: –– the specific functional form of the measured variation; –– the term of the asset returns; and –– the total period used for the estimation. The relationship between historical and implied volatility is considered
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