8902A Measuring Receiver

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JavaScript is currently disabled. This website is best viewed with JavaScript enabled, interactive content that requires JavaScript will not be available. Empirical analysis of option prices has focussed on two related but logically distinct questions. The first is concerned 8902a options trading 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 8902a options trading 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 8902a options trading 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 8902a options trading joint hypothesis in order to test the other. The present study falls within the second category, and is aimed specifically 8902a options trading testing the efficiency 8902a options trading volatility expectations implied in prices of Australian futures and currency options.

We know of no earlier study which examines these particular options 8902a options trading in Australia. For futures options, the study uses the Black-Scholes formula as modified by Black to obtain time series for implied volatilities; for currency 8902a options trading, the Garman-Kohlhagen 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. 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 8902a options trading 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. Skip to content JavaScript is currently disabled.

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JavaScript is currently disabled. This website is best viewed with JavaScript enabled, interactive content that requires JavaScript will not be available. The Black model for pricing options on futures contracts may be written in the following form:. The model assumes that both variances and interest rates are non-stochastic, and that the options cannot be exercised before expiry.

Recent theoretical work by Ramaswamy and Sundaresan , Schaeffer and Schwartz and Hull and White has begun to quantify the effects on option values when these assumptions are loosened; generally speaking the effects appear small when options are near the money or are relatively close to expiry.

For example, the authors cited above compute pricing biases of the order of between zero and 1 per cent in Black-Scholes prices for at-the-money calls when the assumptions are violated. This may be compared with the size of discrepancies arising from likely errors in forecasting volatility.

As an illustration, a 1 percentage point prediction error in estimating volatility on a one year option with true volatility of 0. These magnitudes, and casual observation, suggest that beliefs about volatility are likely to be much more important in determining actual option prices than beliefs about what is the appropriate pricing model, especially for options that are near the money. On this basis, we believe that an empirical focus on forecast accuracy rather than model accuracy is not unwarranted.

We can therefore write:. The cross product terms in the above expression are eliminated by the rationality requirement that future revisions to forecasts are not correlated with current information at any point.

Empirically, some measure of the innovation terms will be needed, and this paper uses the assumption that. A theoretical justification for the above assumption is provided by Samuelson , and strong empirical support is provided in an earlier study, Edey and Elliott , which uses the same data set as the present paper. Equation 5 is a linear prediction equation relating current implied volatility to expected outcomes on observable variables realised in the next period.

Standard efficient markets principles can be used to derive testable restrictions for this equation. The additional extraneous regressors are premultiplied by T-t to ensure that they always have the same order of magnitude as the quantity being forecast.

In the tests reported in section 4 , Z t is taken to include current and past values of. The interpretation of equation 6 is fairly straightforward. Under the efficient markets hypothesis, the current estimate of volatility remaining over the life of the option should be an optimal predictor of realised volatility, expressed as the appropriately weighted sum of next period's estimate and the realised squared price innovation in the next period.

Although equation 6 is similar in spirit to equations tested by other researchers in this context, the exact linear predictive relationship used here has not to our knowledge been previously noted.

Although options on currency futures are traded on the Sydney Futures Exchange, the most active currency options market in Australia is in over-the-counter options, traded mainly in the interbank market. There is an important difference in the expiry date conventions as between the two markets. In futures options, only a small number of standard expiry dates are used coinciding with futures expiry dates , so that a time series of data can be used to obtain a series of observations pertaining to the same expiry date.

In over-the-counter options, the main indicator rates are for standard periods of time ahead of the trading date; thus a time series of data will show a series of options with equal time to expiry. The equivalent of equation 3 in this case is.

The difference between the two regression specifications is that the second imposes the zero restrictions on the expected value of the cross product terms, implied under the null hypothesis.

This effectively removes one source of noise from the left hand side, and should result in improved efficiency in estimation.

Equation 8b is therefore used in the empirical work. To implement the equation, it is assumed that. Implied volatilities are obtained using the Garman-Kohlhagen version of the Black-Scholes model, developed for pricing currency options.

Because the error terms in equations 8a and 8b contain overlapping forecast errors, the method of Hansen and Hodrick is used to correct the estimated standard errors for the resulting serial correlation. Skip to content JavaScript is currently disabled.

Footnote Interest rates are deleted from the formula on the basis that futures options are purchased on margin with no interest opportunity cost. The exact formulas used are: