ARE VOLATILITY EXPECTATIONS CHARACTERIZED BY REGIME SHIFTS? EVIDENCE FROM IMPLIED VOLATILITY INDICES

and foreign exchange markets. Using a bivariate regime-switching model, Hamilton and
Lin (1996) find evidence of higher stock market volatility during periods of economic
recession. Also, Engel and Hakkio (1996) provide evidence based on regime-switching
models that periods of high volatility in the bilateral exchange rates in the European
Monetary System are associated with speculative attacks and subsequent realignment.
Dahlquist and Gray (2000) investigate also the effect of currency target zones in the EMS on
mean reversion and speed of adjustment of short-term interest rates.

The numerical derivation of volatility implied by option prices faces however
impediments stemming from measurement errors, as well as theoretical difficulties
associated with the option pricing model. There is indeed evidence of volatility smiles and
smirks, where different estimates of Black-Scholes implied volatility are derived for options
with different exercise prices and same maturity. This empirical evidence is inconsistent
with the assumption of constant volatility underlying the option pricing theory by
Black-Scholes (1973).³ These difficulties were conducive to the development of a rich
literature of model-free approaches to the estimation of implied volatility. These include
inter alia, the methodology suggested by Ait-Sahalia and Lo (1998) based on polynomials
and splines smoothing, and by Britten-Jones and Neuberger (2000) based on the adjustment
of the volatility process to option prices in the same way that interest rates are fitted to bond
prices.

³ The need to reconcile theoretical assumptions with empirical observations was partly the
impetus behind the development of alternative option valuation models including Hull
and White (1987) and Heston (1993), where the volatility parameter is substituted by the
entire joint probability distribution of returns and volatility changes. More recent studies
by Duan, Gauthier and Simonato (1999) and Ritchken and Trevor (1999) examine option
pricing under GARCH processes.

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