SOME EVIDENCE ON OPTION PRICES AS PREDICTORS OF VOLATILITY
| Published date | 01 November 1992 |
| Author | Malcolm Edey,Graham Elliott |
| Date | 01 November 1992 |
| DOI | http://doi.org/10.1111/j.1468-0084.1992.mp54004006.x |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 54,4(1992)
0305-9049 S3.00
SOME EVIDENCE ON OPTION PRICES AS
PREDICTORS OF VOLATILITY
Malcolm Edey and Graham Elliott t
I. INTRODUCTION
Empirical analysis of option prices has focused on two related but logically
distinct questions. The first is concerned with discriminating between alterna-
tive pricing models. The widely used Black-Scholes model has the attraction
of being both mathematically rigorous and relatively simple to use, since it
specifies option values as a closed function of a small number of parameters
which can be readily observed or estimated. Its validity, however, depends on
a number of restrictive assumptions concerning the stochastic processes
generating prices of the underlying assets. In particular, it assumes that asset
prices follow diffusion processes with constant variances, and this assump-
tion is thought to be unrealistic in many contexts. The Black-Scholes model
has been generalized in a number of important directions to allow for a wider
range of generating processes permitting, for example, price discontinuities
and time-varying volatilities. A number of studies have focused on the per-
formance of such models relative to Black-Scholes in explaining observed
option prices.
A second question concerns the accuracy with which market participants
estimate the parameters needed to implement the option pricing formulas.
Efficient market theory hypothesizes that the market's estimates of these
parameters are statistically optimal, in the sense that they cannot be improved
upon using any information available at the time the expectations are formed.
This hypothesis is directly testable, conditional on assumptions about the
appropriate pricing model. In the case of the Black-Scholes model, for
example, the parameter of prime importance is the expected variance of the
underlying asset price, and given the Black-Scholes assumptions, market
estimates of this parameter can be inferred from observed option premiums
Forecast efficiency can thus be tested by comparing these implied volatilities
with actual price volatilities observed over the subsequent life of the option.
These two empirical approaches are, of course, complementary, each
assuming one part of the joint hypothesis in order to test the other. The
tThe authors wish to thank colleagues at the Reserve Bank of Australia and referees of this
journal for helpful comments.
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