Quantitative method for finance - Essay Example

2. Probability models are models that become relevant when the outcome of interest is not continuous (such as wages per week or stock prices) but rather binary in nature such as, work/not work, survive/not survive etc. In such cases, the simplest possible methodology adoptable is that of the linear probability model or LPM. The response variable of interest, say Y takes the values 0 and 1 only and the approach is to model the expected value of this variable as a linear function of the independent predictor variables X: (ii) The variance of y will be dependent on x.

That is, the model will suffer from conditional heteroscedasticity. This violates the homoscedasticity assumption of OLS. Thus, even though estimates will still be unbiased, the OLS estimator will not be efficient and the estimated standard error will be biased. (iii) The error terms are also binary. They can only take the values of or and thus cannot be normally distributed. Therefore, the assumption of normality of errors is also violated and this in turn would imply problems for typical inferential procedures. (iv) Finally, due to the binary nature of the dependent variable, diminishing returns cannot hold.

Therefore, the functional form restricts the possibility of obtaining diminishing marginal impacts of the independent variable on the dependent variable. 3. (i) If the condition does not hold, then applying OLS is no longer optimum. The assumption implies the error covariances are zero. This is necessary for OLS estimates to have the “Best, Linear, Unbiased” properties. If the error covariances are not zero, then the assumption of the Gauss-Markov theorem are not satisfied and thus, the OLS estimates are no longer best, although they are still unbiased and consistent.

The main problem arises in the context of inferences. 4. (i) If then the series is said to have a unit root. This implies that the series is non-stationary. This essentially translates to the mean and