Modelling the Top40 volatility skew: A principal component analysis approach

Hedge Funds, Asset Managers and Traders that participate in option markets are all exposed to changes in implied volatility, as these changes directly affect the value of an option. In general, implied volatility σK (t, s) is a forecast of an asset's return uncertainty over a specified future time period t , implied from the price of an option (strike level: K, market level: S). Alexander (2001a&b) considers the risk implications of these 'changes in implied volatility'. She constructs a model that explains volatility change (particularly volatility skew) as a result of three dominant effects : trend, slope and convexity. Her model has some appeal in that these independent factors are readily understandable and their effect on an option's price can be calculated independently. Decomposing volatility risk in this way benefits both option traders and risk managers. The intention is to explore these benefits in an emerging market setting by applying Alexander's implied volatility model to the less liquid South African Top40 option market.