Estimating Long-Term Volatility Parameters for Market-Consistent Models

South African Actuarial Journal, Vol. 14, 2014

54 Pages Posted: 17 Jan 2017

See all articles by Emlyn James Flint

Emlyn James Flint

Legae Peresec; Department of Actuarial Science, University of Cape Town

Edru Ochse

Peregrine Securities

Daniel A. Polakow

University of Cape Town (UCT)

Date Written: June 10, 2014

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 (1) 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 (2) 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: econometric volatility models, deterministic volatility models, stochastic volatility models, long-term implied volatility, risk-netrual historical volatility, break-even volatility

JEL Classification: C15, C4, C5, C61, G13

Suggested Citation

Flint, Emlyn James and Ochse, Edru and Polakow, Daniel A., Estimating Long-Term Volatility Parameters for Market-Consistent Models (June 10, 2014). South African Actuarial Journal, Vol. 14, 2014. Available at SSRN: https://ssrn.com/abstract=2890874

Emlyn James Flint (Contact Author)

Legae Peresec ( email )

15 Cavendish Street
Claremont
Cape Town, Western Cape 7700
South Africa
27117227556 (Phone)

HOME PAGE: http://www.legaeperesec.co.za

Department of Actuarial Science, University of Cape Town ( email )

Actuarial Science Section, University of Cape Town
Private Bag X3, Rondebosch
Cape Town, Western Cape 7701
South Africa
+27 21 650 2475 (Phone)

Edru Ochse

Peregrine Securities ( email )

21 Main Road
Claremont
Cape Town, Western Cape 7700
South Africa

Daniel A. Polakow

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

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