Abstract
Corridor implied volatility introduced in Carr and Madan (1998) and recently implemented in Andersen and Bondarenko (2007) is obtained from model-free implied volatility by truncating the integration domain between two barriers. Corridor implied volatility is implicitly linked with the concept that the tails of the risk-neutral distribution are estimated with less precision than central values, due to the lack of liquid options for very high and very low strikes. However, there is no golden choice for the barriers levels’, which will probably change depending on the underlying asset risk neutral distribution. The latter feature renders its forecasting performance mainly an empirical question.The aim of the paper is twofold. First we investigate the forecasting performance of corridor implied volatility by choosing different corridors with symmetric and asymmetric cuts, and compare the results with the preliminary findings in Muzzioli (2010b). Second, we examine the nature of the variance risk premium and shed light on the information content of different parts of the risk neutral distribution of the stock price, by using a model-independent approach based on corridor measures. To this end we compute both realised and model-free variance measures which accounts for drops versus increases in the underlying asset price. The comparison is pursued by using intra-daily synchronous prices between the options and the underlying asset.
Highlights
Volatility modelling and forecasting is essential for asset pricing models, option pricing and hedging and risk management
Corridor implied volatility is implicitly linked with the concept that the tails of the risk-neutral distribution are estimated with less precision than central values, due to the lack of liquid options for very high and very low strikes
The use of asymmetric cuts highlights a weak evidence of superiority of the corridor measure which rely more on put prices on the one which relies more on call prices
Summary
Volatility modelling and forecasting is essential for asset pricing models, option pricing and hedging and risk management. Black-Scholes implied volatility is a model dependent forecast, which relies on the strict assumptions of the Black-Scholes option pricing model about the asset price evolution (Brownian motion) and the constancy of the volatility parameter. Model free implied volatility, introduced by Britten-Jones and Neuberger (2000), represents a valid alternative to Black-Scholes implied volatility, since it does not rely on a particular option pricing model, being consistent with several underlying asset price dynamics. A drawback of model free implied volatility is that it requires a continuum of option prices in strikes, ranging from zero to infinity, assumption which is not fulfilled in the reality of financial markets. The computation of market volatility indexes (see e.g. the VIX index for the Chicago Board Options Exchange, or the V-DAX New for the German stock market), which are closely followed by market participants, is done by operating a truncation of the domain of strike prices once two consecutive strikes with zero bid prices are observed
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