RDP 8902: Option Prices and Implied Volatilities: An Empirical Analysis 1. Introduction

Empirical analysis of option prices has focussed on two related but logically distinct questions. The first is concerned with discriminating between alternative 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 assumption is thought to be unrealistic in many contexts. The Black-Scholes model has been generalised 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 focussed on the performance 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 markets theory hypothesises that the market's estimates of these parameters may be found to be 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 present study falls within the second category, and is aimed specifically at testing the efficiency of volatility expectations implied in prices of Australian futures and currency options. We know of no earlier study which examines these particular options markets in Australia. For futures options, the study uses the Black-Scholes formula as modified by Black (1976) to obtain time series for implied volatilities; for currency options, the Garman-Kohlhagen (1983) version is used. The study derives testable implications relating these implied volatilities to subsequent price movements in the underlying instruments. In doing so, it follows an approach similar to that used in a number of earlier studies using data on U.S. stock options, for example, Schmalensee and Trippi (1978), Latane and Rendleman (1976) and Chiras and Manaster (1978), as well as more recent work by Shastri and Tandon (1986) on currency options. This work has generally found evidence against the hypothesis of forecast efficiency, although the issue remains unclear because of the conditional nature of the hypothesis tests. The present study aims to provide comparable evidence using data on Australian futures and currency options, and will also attempt to test the robustness of the statistical results by examining whether a hypothetical trading rule, aimed at exploiting apparent forecast inefficiencies, generates significant excess returns during the sample period.

Section 2 of the paper derives the tests of forecast efficiency to be used in the empirical work. Section 3 then discusses the data used and section 4 presents the main empirical results. Section 5 reports on an examination of within sample excess returns using a hedged trading strategy based on the estimated volatility predictions. Some conclusions are offered in section 6.