Tipos de opciones de compra de acciones en ingles42 comments
Estrategias de opciones binarias usando promedios moviles
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.
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: